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

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IMPORTANT

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The shortest distance between the point $(\frac{3}{2}, 0)$ and the curve $y = \sqrt{x}, (x > 0)$ , is

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Important Questions on Parabola

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

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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

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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

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 8th April 2018>Q 38

If the tangent at

(1, 7)

to the curve

x^{2} = y - 6

touch the circle

x^{2} + y^{2} + 16 x + 12 y + c = 0

then the value of

c

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 8th April 2018>Q 39

Tangent and normal are drawn at

P (16, 16)

on the parabola

y^{2} = 16 x

, which intersect the axis of the parabola at

A & B

, respectively. If

C

is the center of the circle through the points

P, A & B

and

∠ C P B = θ,

then a value of

\tan θ

is:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 15th April 2018>Q 40

Two parabolas with a common vertex and with axes along the

x

-axis and

y

-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is

3

, then the equation of the common tangent to the two parabolas is :