Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 12

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JEE Advanced

IMPORTANT

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The circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ cuts the parabola $x^{2} = 4 a y$ at point $A_{i} (x_{i}, y_{i}), i = 1, 2, 3, 4$ then

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Important Questions on Parabola

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 13

A circle is drawn to pass through the extremities of latus rectum of the parabola

y^{2} = 8 x

. It is given that this circle also touches the directrix of the parabola. Radius of this circle is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 14

A circle having its centre at

(2, 3)

is cut orthogonally by the parabola

y^{2} = 4 x .

The possible intersection point of these curves can be

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 15

If the length of a focal chord of the parabola

y^{2} = 4 a x

at a distance

b

from the vertex is

c,

then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 16

The angle of intersection between the curves

x^{2} = 4 (y + 1)

and

x^{2} = - 4 (y + 1)

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 17

The equation of a parabola is

y^{2} = 4 x

. If

P (1, 3)

and

Q (1, 1)

are two points in the

X Y

-plane. Then, for the parabola

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 18

A double ordinate parabola

y^{2} = 8 p x

is of length

16 p .

The angle subtended by it at the vertex of the parabola is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 19

The parabola

y^{2} = k x

makes an intercept of length

4

on the line

x - 2 y = 1

, then,

k

is equal to

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 20

Radius of the largest circle which passes through the focus of the parabola

y^{2} = 4 x

and contained in it, is