EASY

JEE Main

IMPORTANT

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The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$ -axis at a distance $R$ and $S (> R)$ respectively from the origin, is :

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Important Questions on Parabola

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 31 August 2021 Shift 2>Q 6

A tangent line

L

is drawn at the point

(2, - 4)

on the parabola

y^{2} = 8 x .

If the line

L

is also tangent to the circle

x^{2} + y^{2} = a^{2},

then

a

is equal to .

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 1 September 2021 Shift 2>Q 7

Consider the parabola with vertex

(\frac{1}{2}, \frac{3}{4})

and the directrix

y = \frac{1}{2} .

Let

P

be the point where the parabola meets the line

x = - \frac{1}{2}

. If the normal to the parabola at

P

intersects the parabola again at the point

Q .

then

(PQ)^{2}

is equal to :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 20 July 2021 Shift 1>Q 8

Let the tangent to the parabola

S : y^{2} = 2 x

at the point

P (2, 2)

meet the

x -

axis at

Q

and normal at it meet the parabola

S

at the point

R

. Then the area (in sq. units) of the triangle

P Q R

is equal to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 20 July 2021 Shift 2>Q 9

If the point on the curve

y^{2} = 6 x,

nearest to the point

(3, \frac{3}{2})

(α, β),

then

2 (α + β)

is equal to _________.

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 July 2021 Shift 1>Q 10

Let a parabola

P

be such that its vertex and focus lie on the positive

x

-axis at a distance

2

and

4

units from the origin, respectively. If tangents are drawn from

O (0, 0)

to the parabola

P

which meet

P

S

and

R

, then the area (in sq. units) of

Δ S O R

is equal to :

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main 16 March 2021 Shift 1>Q 11

If the three normals drawn to the parabola,

y^{2} = 2 x

pass through the point

(a, 0), a \neq 0

, then

a

must be greater than :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main 16 March 2021 Shift 2>Q 12

Let

C

be the locus of the mirror image of a point on the parabola

y^{2} = 4 x

with respect to the line

y = x

. Then the equation of tangent to

C

P (2, 1)

is :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main 17 March 2021 Shift 2>Q 13

Let

L

be a tangent line to the parabola

y^{2} = 4 x - 20

(6, 2) .

L

is also a tangent to the ellipse

\frac{x^{2}}{2} + \frac{y^{2}}{b} = 1,

then the value of

b

is equal to :

The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S(>R) respectively from the origin, is :

Important Questions on Parabola

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The length of the latus rectum of a parabola, whose vertex and focus are on the positive $x$ -axis at a distance $R$ and $S (> R)$ respectively from the origin, is :