EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 8th April 2019 Shift 1>Q 29

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JEE Main

IMPORTANT

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The shortest distance between the line $y = x$ and the curve $y^{2} = x - 2$ 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 - 8th April 2019 Shift 2>Q 30

The tangent to the parabola

y^{2} = 4 x

at the point where it intersects the circle

x^{2} + y^{2} = 5

in the first quadrant, passes through the point:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th April 2019 Shift 2>Q 31

If the line

a x + y = c

, touches both the curves

x^{2} + y^{2} = 1

and

y^{2} = 4 \sqrt{2} x

, then

|c|

is equal to:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th January 2019 Shift 1>Q 32

The shortest distance between the point

(\frac{3}{2}, 0)

and the curve

y = \sqrt{x}, (x > 0)

, is

EASY

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th January 2019 Shift 1>Q 33

If the parabolas

y^{2} = 4 b (x - c)

and

y^{2} = 8 a x

have a common normal, then which one of the following is a valid choice for the ordered triad

(a, b, c)

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th January 2019 Shift 2>Q 34

The length of the chord of the parabola

x^{2} = 4 y

having equation

x - \sqrt{2} y + 4 \sqrt{2} = 0

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 12th April 2019 Shift 2>Q 35

The tangents to the curve

y = {(x - 2)}^{2} - 1

at its points of intersection with the line

x - y = 3,

intersect at the point:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 12th January 2019 Shift 1>Q 36

Let

P (4, - 4)

and

Q (9, 6)

be two points on the parabola,

y^{2} = 4 x

and let

X

be any point on the arc

P O Q

of this parabola, where

O

is the vertex of this parabola, such that the area of

∆ P X Q

is maximum. Then this maximum area (in sq. units) is :

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 12th January 2019 Shift 2>Q 37

The equation of a tangent to the parabola,

x^{2} = 8 y

, which makes an angle

θ

with the positive direction of

x -

axis, is