EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2020>Q 1

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The equation of the latus rectum of a parabola is $x + y = 8$ and the equation of the tangent at the vertex is $x + y = 12 .$ Then, the length of the latus rectum is

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Important Questions on Parabola

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2018>Q 2

Consider the parabola

y^{2} = 4 x

. Let

P

and

Q

be points on the parabola where

P (4, - 4)

and

Q (9, 6) .

Let

R

be a point on the arc of the parabola between

P

and

Q .

Then, the area of

Δ P Q R

is largest when

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2018>Q 3

Let

A, B

be two distinct points on the parabola

y^{2} = 4 x

. If the axis of the parabola touches a circle of radius

r

having

A B

as diameter, the slope of the line

A B

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2020>Q 4

The length of the chord of the parabola

y^{2} = 4 a x (a > 0)

which passes through the vertex and makes an acute angle

α

with the axis of the parabola is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2020>Q 5

If the line

y = x

is a tangent to the parabola

y = a x^{2} + b x + c

at the point

(1, 1)

and the curve passes through

(- 1, 0)

, then

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2018>Q 6

Let

P (a t^{2}, 2 a t), Q, R (a r^{2}, 2 a r)

be three points on a parabola

y^{2} = 4 a x

. If

P Q

is the focal chord and

P K, Q R

are parallel where the co-ordinates of

K

is

(2 a, 0),

then the value of

r

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 11 - Parabola>WBJEE 2018>Q 7

Number of common tangents of

y = x^{2}

and

y = - x^{2} + 4 x - 4

is