HARD

JEE Main

IMPORTANT

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Let a tangent to the curve $y^{2} = 24 x$ meet the curve $x y = 2$ at the points $A$ and $B$ . Then the mid-points of such line segments $A B$ lie on a parabola with the

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Important Questions on Parabola

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 24 January 2023 Shift 2>Q 73

The equations of sides

A B

and

A C

of a triangle

A B C

are

(λ + 1) x + λ y = 4

and

λ x + (1 - λ) y + λ = 0

respectively. Its vertex

A

is on the

y -

axis and its orthocentre is

(1, 2)

. The length of the tangent from the point

C

to the part of the parabola

y^{2} = 6 x

in the first quadrant is

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 January 2023 Shift 1>Q 74

The distance of the point

(6, - 2 \sqrt{2})

from the common tangent

y = m x + c, m > 0

, of the curves

x = 2 y^{2}

and

x = 1 + y^{2}

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 25 January 2023 Shift 2>Q 75

The equations of two sides of a variable triangle are

x = 0

and

y = 3

, and its third side is a tangent to the parabola

y^{2} = 6 x

. The locus of its circumcentre is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 29 January 2023 Shift 2>Q 76

A triangle is formed by the tangents at the point

(2, 2)

on the curves

y^{2} = 2 x

and

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

, and the line

x + y + 2 = 0

. If

r

is the radius of its circumcircle, then

r^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 30 January 2023 Shift 1>Q 77

P (h, k)

be point on the parabola

x = 4 y^{2}

, which is nearest to the point

Q (0, 33)

, then the distance of

P

from the directrix of the parabola

y^{2} = 4 (x + y)

is equal to:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 30 January 2023 Shift 2>Q 78

Let

A

be a point on the

x

-axis. Common tangents are drawn from

A

to the curves

x^{2} + y^{2} = 8

and

y^{2} = 16 x

. If one of these tangents touches the two curves at

Q

and

R

, then

{(Q R)}^{2}

is equal to

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 31 January 2023 Shift 1>Q 79

Let

y = f (x)

represent a parabola with focus

(- \frac{1}{2}, 0)

and directrix

y = - \frac{1}{2}

. Then

S = \{x \in ℝ : \tan^{- 1} (\sqrt{f (x)} + \sin^{- 1} (\sqrt{f (x) + 1})) = \frac{π}{2}\} :

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 31 January 2023 Shift 2>Q 80

Let

S

be the set of all

a \in N

such that the area of the triangle formed by the tangent at the point

P (b, c), b, c \in N

, on the parabola

y^{2} = 2 a x

and the lines

x = b, y = 0

16 {unit}^{2}

, then

\sum_{a \in S} a

is equal to _____ .

Let a tangent to the curve y2 = 24x meet the curve xy = 2 at the points A and B. Then the mid-points of such line segments AB lie on a parabola with the

Important Questions on Parabola

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Let a tangent to the curve $y^{2} = 24 x$ meet the curve $x y = 2$ at the points $A$ and $B$ . Then the mid-points of such line segments $A B$ lie on a parabola with the