EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 26 July 2022 Shift 2>Q 67

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JEE Main

IMPORTANT

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The equation of a common tangent to the parabolas $y = x^{2}$ and $y = - {(x - 2)}^{2}$ is

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Important Questions on Parabola

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 July 2022 Shift 1>Q 68

Let

P (a, b)

be a point on the parabola

y^{2} = 8 x

such that the tangent at

P

passes through the centre of the circle

x^{2} + y^{2} - 10 x - 14 y + 65 = 0

. Let

A

be the product of all possible values of

a

and

B

be the product of all possible values of

b

. Then the value of

A + B

is equal to

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 27 July 2022 Shift 2>Q 69

If the length of the latus rectum of a parabola, whose focus is

(a, a)

and the tangent at its vertex is

x + y = a

, is

16

, then

|a|

is equal to

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 28 July 2022 Shift 1>Q 70

If the tangents drawn at the points

P

and

Q

on the parabola

y^{2} = 2 x - 3

intersect at the point

R (0, 1)

, then the orthocentre of the triangle

P Q R

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 28 July 2022 Shift 2>Q 71

Two tangent lines

l_{1}

and

l_{2}

are drawn from the point

(2, 0)

to the parabola

2 y^{2} = - x

. If the lines

l_{1}

and

l_{2}

are also tangent to the circle

{(x - 5)}^{2} + y^{2} = r^{2}

, then

17 r^{2}

is equal to

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 24 January 2023 Shift 1>Q 72

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

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

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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}

is

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 :