Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 5

MEDIUM

JEE Advanced

IMPORTANT

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$O A$ and $O B$ are two mutually perpendicular chords of $y^{2} = 4 a x, O$ being the origin. Line $A B$ will always passes through the point

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Important Questions on Parabola

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 6

The length of latus rectum of the parabola, whose focus is

(a \sin 2 θ, a \cos 2 θ)

and directrix is the line

y = a

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 7

The point

(a, 2 a)

is an interior point of the region bounded by the parabola

y^{2} = 16 x

and the double ordinate through the focus. Then,

a

belongs to the open interval

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 8

The vertex of a parabola

y^{2} = 8 x

is at the centre of a circle and parabola cuts the circle at ends of its latus rectum. Then, equation of the circle is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 9

A B

is a chord of the parabola

y^{2} = 4 a x

with vertex

A .

B C

is drawn perpendicular to

A B

meeting the axis at

C .

The projection of

B C

on the axis of the parabola is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 10

The circle

x^{2} + y^{2} + 2 λ x = 0, λ \in R,

touches the parabola

y^{2} = 4 x

externally. Then,

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 11

Vertex of the parabola whose parametric equation is

x = t^{2} - t + 1, y = t^{2} + t + 1, t \in R

,

is

HARD

JEE Advanced

IMPORTANT

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

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

HARD

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