MATHS

BOOKS ARIHANT IIT JEE PREVIOUS YEAR MATHS

(HINGLISH)

STRAIGHT LINE AND PAIR OF STRAIGHT LINES

Various Forms Of Straight Line Objective Questions I Only One Correct

Option

1. A straight line at a distance of units from the origin makes

positive intercepts on the coordinate axes and the perpendicular

from the origin to this line makes an angle of with the line

. Then, an equation of the line is

A.

L 4

60∘

x + y = 0 L

x + √3y = 8

B.

C.

D.

Answer: D

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(√3 + 1)x + (√3 − 1)y = 8√2

√3x + y = 8

(√3 − 1)x + (√3 + 1)y = 8√2

2. The equation represents a

straight line lying in

A. second and third quadrants only

B. �rst, second and fourth quadrants

C. �rst, third and fourth quadrants

D. third and fourth quadrants only

Answer:

y = sinx sin(x + 2) − sin2(x + 1)

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3. Lines are drawn parallel to the line , at a distance

from the origin. Then which one of the following points lies on

any of these lines ?

A.

B.

C.

D.

Answer:

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4x − 3y + 2 = 0

3

5

( − , − )1

4

2

3

( − , )1

4

2

3

( , − )1

4

1

3

( , )1

4

1

3

4. The region represented by and is

bounded by a

|x − y| ≤ 2 |x + y| ≤ 2

A. rhombus of side lengths units

B. rhombus of area sq units

C. square of side length units

D. square of area sq units

Answer:

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2

8√2

2√2

16

5. If the two lines and ,

are perpendicular , then the distance of their point

of intersection from the origin is

A.

B.

C.

D.

x + (a − 1)y = 1 2x + a2y = 1

(a ∈ R − {0})

2

5

√2

5

2

√5

√2

5

Answer: D

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6. Slope of a line passing through and intersecting the line,

at a distance of units from , is

A.

B.

C.

D.

Answer: C

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P (2, 3)

x + y = 7 4 P

1 − √5

1 + √5

√7 − 1

√7 + 1

1 − √7

1 + √7√5 − 1

√5 + 1

7. A point R with xcoordinate 4 lies on the line segment joining the

points and . Find the coordinates of the point

R.

A.

B.

C.

D.

Answer:

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P (2, 3, 4) Q(8, 0, 10)

2√21

√53

2√14

6

8. Suppose that the points , and lie on the line

. If a line passing through the points and is

perpendicular to , then equals

(h, k) (1, 2) ( − 3, 4)

L1 L2 (h, k) (4, 3)

L1 k/h

A.

B.

C.

D.

Answer:

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−1

7

1

3

3

0

9. A point on the straight line, which is equidistant

from the coordinate axes will lie only in

A. quadrant

B. quadrant

C. and quadrant

D. , and quadrant

3x + 5y = 15

IV

I

I II

I II IV

Answer:

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10. If a straight line passing through the point is such

that its intercepted portion between the coordinate axes is bisected

at , then its equation is

A.

B.

C.

D.

Answer:

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P ( − 3, 4)

P

x − y + 7 = 0

4x − 3y + 24 = 0

3x − 4y + 25 = 0

4x + 3y = 0

11. A line is perpendicular to the line and passes

through the points and (7, 17) beta

35/3 -35/3 5 -5`

A.

B.

C.

D.

Answer:

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2x − 3y + 5 = 0

(15, β) thenvalueof

willbeequal → (A) (B) (C) (D)

35

3

−5

−35

3

5

12. If in parallelogram , the coordinate of , and are

respectively , and , then the equation of the

diagonal is

ABDC A B C

(1, 2) (3, 4) (2, 5)

AD

A.

B.

C.

D.

Answer:

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3x + 5y − 13 = 0

3x − 5y + 7 = 0

5x − 3y + 1 = 0

5x + 3y − 11 = 0

13. Tangent at on the curve , also passes through the

point (a) (b) (c) (d)

A.

B.

C.

D.

(1, e) y = xex2

( , 2e)43

( , e)5

3( , 3e)

43

( , 3e)3

4

( , 2e)43

(3, 6e)

(2, 3e)

( , 2e)5

3

Answer:

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14. Two sides of a parallelogram are and . If the

diagonals meet at then which of the following can be one of

the vertex of parallelogram. (a) (3,6) (b) (0,0) (c) (d)

A.

B.

C.

D.

Answer:

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x + y = 3 y − x = 3

(2, 4)

(1, − 2) (2, 3)

(3, 6)

(2, 6)

(2, 1)

(3, 5)

15. The shortest distance between the point and the curve

, is

A.

B.

C.

D.

Answer:

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( , 0)3

2

y = √x, (x > 0)

3

2

5

4

√3

2

√5

2

16. If the point intersects the -axis at the point

and the -axis at the point , then the incentre of the triangle

, where is the origin, is

A.

3x + 4y − 24 = 0 X

A Y B

OAB O

(4, 3)

B.

C.

D.

Answer:

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(3, 4)

(4, 4)

(2, 2)

17. A point P moves on line If and

are �xed points, then the locus of the centroid of

is a line: (a) with slope (b) parallel to y-axis (c) with

slope (d) parallel to x-axis

A. with slope

B. with slope

C. parallel to -axis

D. parallel to -axis

2x − 3y + 4 = 0 Q(1, 4)

R(3, − 2)

△ PQR3

22

3

2

3

3

2

Y

X

Answer:

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18. The straight line through a �xed point (2,3) intersects the

coordinate axes at distinct point P and Q. If O is the origin and the

rectangle OPRQ is completed then the locus of R is

A.

B.

C.

D.

Answer:

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3x + 2y = 6

2x + 3y = xy

3x + 2y = xy

3x + 2y = 6xy

19. Let be an integer such that the triangle with vertices

and has area units. Then the

orthocentre of this triangle is at the point : (2)

(3) (4)

A.

B.

C.

D.

Answer:

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k

(k, − 3k), (5, k) ( − k, 2) 28sq.

(1, − )3

4(2, )

1

2

(2, − )1

2(1, )

3

4

(2, − )1

2

(1, )3

4

(1, − )3

4

(2, )1

2

20. Let a,b, c and d be non-zero numbers. If the point of intersection

of the lines and lies in the4ax + 2ay + c = 0 5bx + 2by + d = 0

fourth quadrant and is equidistant from the two axes, then

A.

B.

C.

D.

Answer:

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2bc − 3ad = 0

2bc + 3ad = 0

2ad − 3bc = 0

3bc + 2ad = 0

21. Let be the median of the triangle with vertices

Then equation of the line passing

through and parallel to is

A.

B.

PS

P (2, 2), Q(6, − 1)andR(7, 3)

(1, − 1) PS 2x − 9y − 7 = 0

2x − 9y − 11 = 0 2x + 9y − 11 = 0 2x + 9y + 7 = 0

4x − 7y − 11 = 0

2x + 9y + 7 = 0

C.

D.

Answer:

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4x + 7y + 3 = 0

2x − 9y − 11 = 0

22. The x-coordiante of the incentre of the triangle that has the

coordiantes of mid points of its sides as (0,1),(1,1) and (1,0) is:

A.

B.

C.

D.

Answer:

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2 + √2

2 − √2

1 + √2

1 − √2

23. A straight line L through the point (3,-2) is inclined at an angle

to the line If L also intersects the x-axis then the

equation of L is

A.

B.

C.

D.

Answer:

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60∘ √3x + y = 1

y + √3x + 2 − 3√3 = 0

y − √3x + 2 + 3√3 = 0

√3y − x + 3 + 2√3 = 0

√3y + x − 3 + 2√3 = 0

24. The locus of the orthocentre of the triangle formed by the lines

and(1 + p)x − py + p(1 + p) = 0, (1 + q)x − qy + q(1 + q) = 0

y = 0, where , is (A) a hyperbola (B) a parabola (C) an ellipse

(D) a straight line

A. a hyperbola

B. a parabola

C. an ellipse

D. a straight line

Answer:

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p ≠ ⋅ q

25. Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle OPQ. The

point R inside the triangles OPQ is such that the triangles OPR, PQR,

OQR are of equal area. The coordinates of R are (1) (2)

(3) (4)

A.

( , 3)43

(3, )2

3(3, )

43

( , )43

2

3

( , 3)43

B.

C.

D.

Answer:

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(3, )2

3

(3, )43

( , )43

2

3

26. The orthocentre of the triangle with vertices and

is (b) (d)

A.

B.

C.

D.

Answer:

(0, 0), (3, 4),

(4, 0) (3, )5

4(3, 12) (3, )

3

4(3, 9)

(3, )5

4

(3, 12)

(3, )3

4

(3, 9)

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27. The number of integer values of for which the x-coordinate of

the point of intersection of the lines, and

is also an integer is 2 (b) 0 (c) 4 (d) 1

A.

B.

C.

D.

Answer:

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m,

3x + 4y = 9 y = xm + 1

2

0

4

1

28. A straight line through the origin 'O' meets the parallel lines

and at points P and Q respectively. Then4x + 2y = 9 2x + y = − 6

the point 'O' divides the segment PQ in the ratio

A.

B.

C.

D.

Answer:

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1: 2

3: 4

2: 1

4: 3

29. Find the incentre of the triangle with vertices and

A.

B.

C.

(1, √3), (0, 0)

(2, 0)

(1, )√3

2

( , )2

3

1

√3

( , )2

3

√3

2

D.

Answer:

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(1, )1

√3

30. Let be a regular hexagon inscribed in a circle of

unit radius. Then the product of the lengths the line segments

and is

A.

B.

C.

D.

Answer:

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A0A1A2A3A4A5

A0A1, A0A2 A0A4

3/4

3√3

3

3√3

2

31. If the vertices P, Q, R of a triangle PQR are rational points, which

of the following points of the triangle POR is (are) always rational

point(s) ?

A. centroid

B. incentre

C. circumcentre

D. orthocentre

Answer:

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32. If and are the vertices of a

parallelogram then (b)

(d)

P (1, 2)Q(4, 6), R(5, 7), S(a, b)

PQRS, a = 2, b = 4 a = 3, b = 4

a = 2, b = 3 a = 1 or b = − 1

A.

B.

C.

D.

Answer:

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a = 2, b = 4

a = 3, b = 4

a = 2, b = 3

a = 3, b = 5

33. The diagonals of a parallelogram PQRS are along the lines x+3y

=4 and 6x-2y = 7, Then PQRS must be :

A. rectangle

B. square

C. cyclic quadrilateral

D. rhombus

Answer:

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34. The graph of the function, is

A. a straight line passing through with slope

B. a straight line passing through

C. a parabola with vertex

D. a straight line passing through the point and

parallel to the -axis

Answer:

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cos x cos(x + 2) − cos2(x + 1)

(0, − sin2 1) 2

(0, 0)

(1, − sin2 1)

( , − sin2 1)π

2

X

35. The orthocentre of the triangle formed by the lines and

is

A.

B.

C.

D.

Answer:

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xy = 0

x + y = 1

( , )1

2

1

2

( , )1

3

1

3

(0, 0)

( , )1

4

1

4

36. If the sum of the distances of a point from two perpendicular

lines in a plane is 1, then its locus is a square (b) a circle a straight

line (d) two intersecting lines

A. square

B. circle

C. straight line

D. two intersecting lines

Answer:

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37. Line has intercepts and on the coordinate axes. When, the

axes area rotated through a given angle, keeping the origin �xed,

the same line has intercepts and , then

A.

B.

C.

D.

L a b

L p q

a2 + b2 = p2 + q2

+ = +1

a2

1

b2

1

p2

1

q2

a2 + p2 = b2 + q2

+ = +1

a2

1

p2

1

b2

1

q2

Answer:

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38. If are three given points,

then the locus of the points S satisfying the relation,

is -

A. a straight line parallel to -axis

B. a circle passing through the origin

C. a circle with the centre at the origin

D. a straight line parallel to -axis

Answer:

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P = (1, 0); Q = ( − 1.0)&R = (2, 0)

SQ2 + SR2 = 2SP 2

X

Y

39. The point (4, 1) undergoes the following three transformations

successively: (a) Re�ection about the line y = x (b) Translation

through a distance 2 units along the positive direction of the x-axis.

(c) Rotation through an angle about the origin in the anti

clockwise direction. The �nal position of the point is given by the co-

ordinates.

A.

B.

C.

D.

Answer:

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π

4

( , )1

√2

7

√2

( − √2, 7√2)

( − , )1

√2

7

√2

(√2, 7√2)

Various Forms Of Straight Line Objective Questions Ii Only Or More

Than One Correct Option

40. The points , . and are

A. collinear

B. vertices of a rectangle

C. vertices of a parallelogram

D. None of the above

Answer:

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( − a, − b) (0, 0) (a, b) (a2, ab))

1. Let Consider the system of linear equations

Which of the �ollowing statement (s) is

(are) correct?

a, λ, μ ∈ R,

ax + 2y = λ3x − 2y = μ

A. If then the system has in�nitely many solution for all

values of and

B. If then the system has a unique solution for all

values of and

C. If , then the system has in�nitely many solution for

D. If , then the system has no solution for

Answer:

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a = − 3

λ μ

a = − 3

λ μ

λ + μ = 0

a = − 3

λ + μ ≠ 0 a = − 3

2. For , if the distance between and the point of

intersection of the line and is

less than then, (A) (B) (C)

(D)

a > b > c > 0 (1, 1)

ax + by − c = 0 bx + ay + c = 0

2√2 a + b − c > 0 a − b + c < 0

a − b + c > 0 a + b − c < 0

A.

B.

C.

D.

Answer:

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a + b − c > 0

a − b + c < 0

a − b + c > 0

a + b − c < 0

3. All points lying inside the triangle formed by the points (1. 3). (5, 0)

and (-1, 2) satisfy (A) (B) (C)

(D)

A.

B.

C.

D.

3x + 2y ≥ 0 2x + y − 13 ≥ 0

2x − 3y − 12 ≤ 0 −2x + y ≥ 0

3x + 2y ≥ 0

2x + y − 13 ≥ 0

2x − 3y − 12 ≤ 0

−2x + y ≥ 0

Various Forms Of Straight Line Fill In The Blanks

Answer:

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1. Let the algebraic sum of the perpendicular distance from the

points (2, 0), (0,2), and (1, 1) to a variable straight line be zero. Then

the line passes through a �xed point whose coordinates are___

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2. The orthocenter of the triangle formed by lines

lines in quadrant

number

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x + y = 1, 2x + 3y = 6 and 4x − y + 4 = 0

Various Forms Of Straight Line True False

3. If are in then the straight line will

always pass through a �xed point whose coordinates are______

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a, bandc AP , ax + by + c = 0

4. is the re�ection of in the line whose equation

is

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y = 10x y = log10 x

1. The lines and , cut the

coordinate axes at concyclic points.

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2x + 3y + 19 = 0 9x + 6y − 17 = 0

Various Forms Of Straight Line Analytical Desriptive Questions

2. No tangent can be drawn from the point to the

circumcircle of the triangle with vertices

.

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( , 1)5

2

(1, √3), (1, − √3), (3, − √3)

3. The line 5x + 4y = 0 passes through the point of intersection of

straight lines (1) x+2y-10 = 0, 2x + y =-5

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1. A straight line L through the origin meets the lines and

at P and Q respectively. Through P and Q two straight

x + y = 1

x + y = 3

lines , and are drawn, parallel to and

respectively. Lines and intersect at R. Locus of R, as L varies, is

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L1 L2 2x − y − 5 3x + y5

L1 L2

2. A straight line l with negative slope passes through (8,2) and cuts

the coordinate axes at P and Q. Find absolute minimum value of

''OP+OQ where O is the origin-

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3. For points of the coordinate

plane, a new distance is de�ned by

Let and .

Prove that the set of points in the �rst quadrant which are

equidistant (wrt new distance) from and consists of the union

P = (x1, y1) and Q = (x2, y2)

d(P , Q)

d(P , Q) = |x1 − x2| + |y1 − y2|. O(0, 0) A = (3, 2)

O A

of a line segment of �nite length and an in�nite ray. Sketch this set

in a labelled diagram.

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4. A rectangle PQRS has its side PQ parallel to the line and

vertices , and on the lines ,and ,

respectively. Find the locus of the vertex .

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y = mx

P , Q S y = a, x = b x = − b

R

5. A line through meets the lines

at the points

rspectively, if �nd the

equation of the line.

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A( − 5, − 4)

x + 3y + 2 = 0, 2x + y + 4 = 0andx − y − 5 = 0

B, CandD ( )2

+ ( )2

= ( )2

15

AB

10

AC

6

AD

6. Determine all the values of for which the point lies

inside the triangle formed by the lines.

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α (α, α2)

2x + 3y − 1 = 0

x + 2y − 3 = 0 5x − 6y − 1 = 0

7. Find the equation of the line passing through the point and

making an inter length units between the lines and

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(2, 3)

3 y + 2x = 2

y + 2x = 5.

8. The st. lines interrect at a point

. On these linepoints B and C are chosen so that

. Find the possible eqns of the line BC pathrough the

point

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3x + 4y = 5 and 4x − 3y = 15

A(3, − 1)

AB = AC

(1, 2)

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9. A line cuts the x-axis at and the y-axis at A

variable line PQ is drawn perpendicular to AB cutting the x-axis in P

and the y-axis in Q. If AQ and BP intersect at R, �nd the locus of R

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A(7, 0) B(0, − 5)

10. let ABC be a triangle with AB=AC. If D is the mid-point of BC, E the

foot of the perpendicular drawn from D to AC, F is the mid-point of

DE. Prove that AF is perpendicular to BE.

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11. The equations of the perpendicular bisectors of the sides

of triangle are and ,ABandAC ABC x − y + 5 = 0 x + 2y = 0

respectively. If the point is , then �nd the equation of the

line

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A (1, − 2)

BC.

12. One of the diameter of a circle circumscribing the rectangle ABCD

is , If A and B are the points and

respectively, then the area of rectangle is

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4y = x + 7 ( − 3, 4) (5, 4)

13. Two sides of a rhombus ABCD are parallel to the lines y = x + 2

and y = 7x + 3 If the diagonals of the rhombus intersect at the point

(1, 2) and the vertex A is on the y-axis, then vertex A can be

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14. Two equal sides of an isosceles triangle are given by

and , and its third side passes through

the point . Find the equation of the third side.

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7x − y + 3 = 0 x + y = 3

(1, − 10)

15. The vertices of a triangle are

, , .

Find the orthocentre of the triangle.

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[at1t2, a(t1 + t2)] [at2t3, a(t2 + t3)] [at3t1, a(t3 + t1)]

16. The ends A and B of a straight line segment of constant length c

slide upon the �xed rectangular axes OX and OY, respectively. If the

rectangle OAPB be completed, then the locus of the foot of the

perpendicular drawn from P to AB is

W h Vid S l i

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17. . The points (1,3), (5, 1) are the opposite vertices of a rectangle.

The other two vertices lie on the line . Find c and

remaining two vertices.

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y = 2x + c

18. Two vertices of a triangle are and If the

orthocentre of the triangle is the origin, �nd the coordinates of the

third point.

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(5, − 1) ( − 2, 3)

19. One side of a rectangle lies along the line Two

of its vertices are Find the equations of the other

three sides.

4x + 7y + 5 = 0.

( − 3, 1)and(1, 1).

Various Forms Of Straight Line Integer Answer Type Question

Angle Between Straight Line And Equation Of Angle Bisector Objective

Questions Ii One Or More Than One Correct Option

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1. For a point in the plane, let be the distances of

the point from the lines respectively. The

area of the region consisting of all points lying in the �rst

quadrant of the plane and satisfying is

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P d1(P )andd2(P )

P x − y = 0andx + y = 0

R P

2 ≤ d1(P ) + d2(P ) ≤ 4,

1. A ray of light along gets re�ected upon reaching x-

axis, the equation of the re�ected ray is

x + √3y = √3

A.

B.

C.

D.

Answer:

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y = x + √3

√3y = x − √3

y = √3x − √3

√3y = x − 1

2. Consider three points ,

, and ,

where Then

A. lies on the line segment

B. lies on the line segment

C. lies on the line segment

D. are non-colinear.

P = ( − sin(β − α), − cos β)

Q = (cos(β − α), sinβ) R = ((cos(β − α + θ), sin(β − θ))

0 < α, β, θ <π

4

P RQ

Q PR

R QP

P , Q, R

Angle Between Straight Line And Equation Of Angle Bisector Assertion

And Reason

Answer:

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3. Let P = (-1, 0), Q = (0, 0) and R = (3, ) be three points. The

equation of the bisector of the angle PQR

A.

B.

C.

D.

Answer:

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3√3

x + y = 0√3

2

x + √3y = 0

√3x + y = 0

x + y = 0√3

2

1. Lines and intersect the line

at and respectively. The bisector of the acute

angle between and intersects at .

Statement I The ratio equals .

Because

Statement II In any triangle, bisector of an angle divides the triangle

into two similar triangles.

A. Statement I is true, Statement II is also true, Statement II is

correct explanation of Statement I

B. Statement I is true, Statement II is also true, Statement II is not

the correct explanation of Statement I

C. Statement I is true , Statement II is false

D. Statement I is false , Statement II is true

Answer:

L1 : y − c = 0 L2 : 2x + y = 0

L3 : y + 2 = 0 P Q

L1 L2 L3 R

PR :RQ 2√2: √5

Angle Between Straight Line And Equation Of Angle Bisector Fill In The

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Angle Between Straight Line And Equation Of Angle Bisector Analytical

Desriptive Questions

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1. The vertices of a triangle are .

The equation of the bisector of the angle ABC

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A( − 1, − 7), B(5, 1) and C(1, 4)

1. The area of the triangle formed by the intersection of a line

parallel to x-axis and passing through P (h, k) with the lines y = x and

x + y = 2 is . Find the locus of the point P.

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4h2

Area And Family Of Concurrent Lines Objective Questions I Only One

Correct Option

2. The equation of the line which bisects the obtuse angle between

the line and is

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x − 2y + 4 = 0 4x − 3y + 2 = 0

3. lines and intersect at

the point and make a angle between each other. �nd the

equation of a line di�erent from which passes through and

makes the same angle with

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L1 : ax + by + c = 0 L2 : lx + my + n = 0

P θ

L L2 P

θ L1

1. 21. If a vertex of a triangle is (1, 1) and the midpoints of two sides of

the triangle through this vertex are (-1, 2) and (3, 2), then the

centroid of the triangle is

A.

B.

C.

D.

Answer:

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(1, )73

( , 2)1

3

( , 1)1

3

( , )1

3

5

3

2. If represent a family fo staright lines such that

then (a) All lines are parallel (b) All lines are

incosistance (c) All lines are concurrent at (d) All lines are

concurrent at

px + qx + r = 0

3p + 2q + 4r = 0

( , )3

4

1

2

(3, 2)

A. Each lines passes through the origin.

B. The lines are concurrent at the point

C. The lines are all parallel

D. The lines are not concurrent

Answer:

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( , )3

4

1

2

3. Two sides of a rhombus are along the lines, and

. If its diagonals intersect at , then

which one of the following is a vertex of this rhombus ? (1)

(2) (3) (4)

A.

B.

C.

x − y + 1 = 0

7x − y − 5 = 0 ( − 1, − 2)

( − 3, − 9) ( − 3, − 8) ( , − )1

3

8

3( − , − )

10

373

( − 3, − 9)

( − 3, − 8)

( , − )1

3

8

3

D.

Answer:

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( − , − )10

373

4. Area of the parallelogram formed by the lines y = mx, y = mx + 1,y =

nx and y =nx+1 equals to

A.

B.

C.

D.

Answer:

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|m + n|

(m − n)2

2

|m + n|

1

|m + n|

1

|m − n|

5. The points , and are vertices of

A. an obtuse angled triangle

B. an acute angled triangle

C. a right angled triangle

D. None of the above

Answer:

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(0, )8

3(1, 3) (82, 30)

6. The straight line , ,

form a triangle which is

A. isoscles

B. equilateral

C. right angled

x + y = 0 3x + y − 4 = 0 x + 3y − 4 = 0

D. None of the above

Answer:

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7. Given the four lines with the equations

, ,

, , then

A. they are all concurrent

B. they are the sides of a quadrilateral

C. only three lines are concurrent

D. None of the above

Answer:

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x + 2y − 3 = 0 3x + 4y − 7 = 0

2x + 3y − 4 = 0 4x + 5y − 6 = 0

Area And Family Of Concurrent Lines Objective Questions Ii Only Or

More Than One Correct Option

Area And Family Of Concurrent Lines Match The Columns

1. Three lines , and

are concurrent , if

A.

B.

C.

D. None of these

Answer:

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px + qy + r = 0 qx + ry + p = 0

rx + py + q = 0

p + q + r = 0

p2 + q2 + r2 = pr + rq

p3 + q3 + r3 = 3pqr

Area And Family Of Concurrent Lines Fill In The Blanks

Area And Family Of Concurrent Lines True False

1.

are concurrent if k=

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L1 = x + 3y − 5 = 0, L2 = 3x − ky − 1 = 0, L3 = 5x + 2y − 12 = 0

1. The set of lines , where is

concurrent at the point…

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ax + by + c = 0 3a + 2b + 4c = 0

Area And Family Of Concurrent Lines Analytical Desriptive Questions

1. If , then the two triangles with vertices

, , and , , must be

congruent.

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∣∣∣∣∣

x1 y1 1

x2 y2 1

x3 y3 1

∣∣ ∣ ∣∣

=

∣∣ ∣∣

a1 b1 1

a2 b2 1

a3 b3 1

∣∣ ∣∣

(x1, y1) (x2, y2) (x3, y3) (a1, b1) (a2, b2) (a3, b3)

1. Prove that the altitudes of a triangle are concurrent.

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2. The coordinates of are , ,

respectively and is any point . Show that the ratio of the

areas of the triangles and is .

W t h Vid S l ti

A, B, C (6, 3) ( − 3, 5) (4, − 2)

P (x, y)

ΔPBC ΔABC∣∣∣

∣∣∣

x + y − 2

7

Homogeneous Equation Of Pair Of Straight Lines Objective Questions I

Only One Correct Option

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3. A straight line is perpendicular to the line . The area

of the triangle formed by line and the coordinate axes is 5. Find

the equation of line

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L 5x − y = 1

L,

L.

1. Let 'a' and 'b' be non-zero real numbers. Then, the equation

represents :

A. four straight lines, when and , are of the same sign

B. two straight lines and circle, when and is of sign

opposite to that of

(ax2 + by2 + c)(x2 − 5xy + 6y2)

c = 0 a b

a a = b c

a

C. two straight lines and a circle, when and is of sign

opposite to that of

D. a circle and an ellipse, when and are of the same sign and

is of sign opposite to that of

Answer:

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a = b c

a

a b c

a

2. Area of the triangle formed by the line and angle

bisectors of the pair of straight lines is

b. c. d.

A. sq units

B. sq units

C. sq units

D. sq units

x + y = 3

x2 − y2 + 2y = 1 2sq.units

4sq.units 6sq

.units 8sq

.units

2

4

6

8

Homogeneous Equation Of Pair Of Straight Lines Analytical Desriptive

Questions

General Equation Of Pair Of Straight Lines Objective Questions I Only

One Correct Option

Answer:

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1. Show that all chords of the curve which

subtend a right angle at the origin, pass through a �xed point. Find

the coordinates of the point.

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3x2 − y2 − 2x + 4y = 0,

1. 1. Let PQR be a right angled isosceles triangle, right angled at P

(2,1). If the equation of the line QR is 2x + y 3, then the equation

representing the pair of (1999, 2M) lines P and PR is

A.

B.

C.

D.

Answer:

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3x2 − 3y2 + 8xy + 20x + 10y + 25 = 0

3x2 − 3y2 + 8xy − 20x − 10y + 25 = 0

3x2 − 3y2 + 8xy + 10x + 15y + 20 = 0

3x2 − 3y2 − 8xy − 10x − 15y − 20 = 0