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

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JEE Main

IMPORTANT

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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

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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 - 3rd April 2016>Q 45

Let

P

be the point on the parabola,

y^{2} = 8 x

which is at a minimum distance from the center

C

of the circle

x^{2} + {(y + 6)}^{2} = 1

. Then the equation of the circle, passing through

C

and having its center at

P

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th April 2016>Q 46

P

and

Q

are two distinct points on the parabola,

y^{2} = 4 x

, with parameters

t

and

t_{1}

, respectively. If the normal at

P

passes through

Q

, then the minimum value of

t_{1}^{2}

, is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 10th April 2015>Q 47

If the tangent to the conic,

y - 6 = x^{2}

at

(2, 10)

touches the circle,

x^{2} + y^{2} + 8 x - 2 y = k

(for some fixed

k

) at a point

(α, β);

then

(α, β)

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 4th April 2015>Q 48

Let

O

be the vertex and

Q

be any point on the parabola,

x^{2} = 8 y

. If the point

P

divides the line segment

O Q

internally in the ratio

1 : 3

, then the locus of

P

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 11th April 2015>Q 49

If

P Q

be a double ordinate of the parabola,

y^{2} = - 4 x,

where

P

lies in the second quadrant. If

R

divides

P Q

in the ratio

2 : 1,

then the locus of

R

is:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 19th April 2014>Q 50

A chord is drawn through the focus of the parabola

y^{2} = 6 x

such that its distance from the vertex of this parabola is

\frac{\sqrt{5}}{2}

, then its slope can be

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IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 6th April 2014>Q 51

The slope of the line touching both the parabolas

y^{2} = 4 x

and

x^{2} = - 32 y

is

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 16 - Parabola>JEE Main - 7th April 2013>Q 52

Given : A circle,

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

and a parabola,

y^{2} = 4 \sqrt{5} x

.

Statement - I : An equation of a common tangent to these curves is

y = x + \sqrt{5}

.

Statement - II : If the line,

y = m x + \frac{\sqrt{5}}{m} (m \neq 0)

is their common tangent, then

m

satisfies

m^{4} - 3 m^{2} + 2 = 0

.