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

HARD

JEE Main

IMPORTANT

Earn 100

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

50% studentsanswered this correctly

Important Questions on Parabola

HARD

JEE Main

IMPORTANT

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

If

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

is

16 {unit}^{2}

, then

\sum_{a \in S} a

is equal to _____ .

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 1 February 2023 Shift 2>Q 81

If the

x

-intercept of a focal chord of the parabola

y^{2} = 8 x + 4 y + 4

is

3

, then the length of this chord is equal to _____ .