Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 36

HARD

JEE Advanced

IMPORTANT

Earn 100

The image of the parabola $y^{2} = 4 x$ about the line $x - y + 1 = 0$ is

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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>Entrances Gallery>Q 37

The angle between the tangents drawn from the point

(4, 4)

to the parabolas

y^{2} = 4 x

and

x^{2} = 4 y,

is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 38

The line

2 x + y + k = 0

is a normal to the parabola

y^{2} = - 8 x,

if

k

is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 39

The equation

y^{2} + 4 x + 4 y + k = 0

represents a parabola, whose latus rectum is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 40

Let

P

and

Q

be the points on the parabola

y^{2} = 4 x,

so that the line segment

P Q

subtends right angle at the vertex. If

P Q

intersects the axis of the parabola at

R

then the distance of the vertex from

R

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 41

If the straight lines

y = \pm x

intersect the parabola

y^{2} = 8 x

in points

P

and

Q,

then the length of

P Q

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 42

The sum of the reciprocals of focal distances of a focal chord

P Q

of

y^{2} = 4 a x

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 44

The distance between the vertex of the parabola

y = x^{2} - 4 x + 3

and the centre of the circle

x^{2} = 9 - {(y - 3)}^{2},

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 45

The parabola

y^{2} = 4 x

and the circle

x^{2} + y^{2} - 6 x + 1 = 0

will