EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2020>Q 17

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IMPORTANT

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Let each of the equations $x^{2} + 2 x y + a y^{2} = 0$ and $a x^{2} + 2 x y + y^{2} = 0$ represent two straight lines passing through the origin. If they have a common line, then the other two lines are given by

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Important Questions on Straight Line

EASY

WBJEE

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2020>Q 1

A straight line through the origin

O

meets the parallel lines

4 x + 2 y = 9

and

2 x + y + 6 = 0

at

P

and

Q

respectively. The point

O

divides the segment

P Q

in the ratio

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2018>Q 2

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

h^{2}

. The locus of the point

P

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2020>Q 3

A line cuts the

x

-axis at

A (7, 0)

and the

y

-axis at

B (0, - 5)

. A variable line

P Q

is drawn perpendicular to

A B

cutting the

x

-axis at

P (a, 0)

and the

y

-axis at

Q (0, b)

. If

A Q

and

B P

intersect at

R

, the locus of

R

is

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2019>Q 4

If

P (0, 0), Q (1, 0)

and

R (\frac{1}{2}, \frac{\sqrt{3}}{2})

are three given points, then the centre of the circle for which the lines

P Q, Q R

and

R P

are the tangents is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2018>Q 5

The point

Q

is the image of the point

P (1, 5)

about the line

y = x

and

R

is the image of the point

Q

about the line

y = - x

. The circumcentre of the

Δ P Q R

is

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2018>Q 6

Without changing the direction of the axes, the origin is transferred to the point

(2, 3)

Then the equation

x^{2} + y^{2} - 4 x - 6 y + 9 = 0

changes to

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2020>Q 7

The equation $r \cos (θ - \frac{π}{3}) = 2$ represents

EASY

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2020>Q 8

The equation of the straight line passing through the point

(4, 3)

and making intercepts on the coordinate axes whose sum is

- 1

is