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

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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 Questions on Straight Line

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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

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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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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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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

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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

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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

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

A variable line passes through a fixed point

(x_{1}, y_{1})

and meets the axes at

A

and

B .

If the rectangle

O A P B

be completed, the locus of

P

is, (

O

being the origin of the system of axes).

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 9 - Straight Line>WBJEE 2018>Q 10

The angular points of a triangle are

A (- 1, - 7)

,

B (5, 1)

and

C (1, 4)

. The equation of the bisector of the angle

∠ A B C

is