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

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JEE Main

IMPORTANT

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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 :

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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 - 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:

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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 :

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 16th April 2018>Q 41

Let

P

be a point on the parabola

x^{2} = 4 y

. If the distance of

P

from the center of the circle

x^{2} + y^{2} + 6 x + 8 = 0

is minimum, then the equation of the tangent to the parabola at

P

is

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 8th April 2017>Q 42

If the common tangents to the parabola,

x^{2} = 4 y

and the circle,

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

intersect at the point

P

, then the distance of

P

from the origin (units), is:

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JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 9th April 2017>Q 43

If

y = m x + c

is the normal at a point on the parabola

y^{2} = 8 x

whose focal distance is

8

units, then

|c|

is equal to:

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 3rd April 2016>Q 44

The centres of those circles which touch the circle,

x^{2} + y^{2} - 8 x - 8 y - 4 = 0,

externally and also touch the

x

- axis, lie on