Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 71

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JEE Advanced

IMPORTANT

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Length of the shortest normal chord of the parabola $y^{2} = 4 x$ is

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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 72

Tangent and normal drawn to parabola at

A (a t^{2}, 2 a t), t \neq 0,

meet

X

-axis at points

B

and

D

respectively. If the rectangle

A B C D

is completed, then the locus of

C

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 73

Normals

P O, P A

and

P B, O

being the origin, are drawn to

y^{2} = 4 x

from

P (h, 0) .

If

∠ A O B = \frac{π}{2},

then area of quadrilateral

O A P B

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 75

The radius of the circle whose centre is

(- 4, 0)

and which cuts the parabola

y^{2} = 8 x

at

A

and

B

, such that its common chord

A B

subtends a right angle at the vertex of the parabola is equal to

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 76

If the line

y = m x + 1

is a tangent to

y^{2} = 4 m x,

then the distance of this tangent from the parallel normal is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 77

A B

is a double ordinate of the parabola

y^{2} = 4 a x .

Tangents drawn to parabola at

A

and

B

meets

Y

-axis at

A_{1}

and

B_{1},

respectively. If the area of trapezium

A A_{1} B_{1} B

is equal to

24 a^{2},

then the angle subtended by

A_{1} B_{1}

at the focus of parabola 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 78

Maximum number of common normals of

y^{2} = 4 a x

and

x^{2} = 4 b y

can be equal to

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 79

If two different tangents of

y^{2} = 4 x

are the normals to

x^{2} = 4 b y,

then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 80

Two parabolas with the same axis, focus of each being exterior to the other and the latus rectum being

4 a

and

4 b .

The locus of middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a/an