Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 43

HARD

JEE Advanced

IMPORTANT

Earn 100

A variable parabola having length of its latus rectum equal to $4 a$ and having its axis parallel to $X$ -axis drawn in such a way that it always touches the parabola $y^{2} = 4 a x$ . Then, the locus of vertex of the variable parabola is

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Important Questions on Parabola

HARD

JEE Advanced

IMPORTANT

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

Set of values of

m

for which a chord of slope

m

of the circle

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

touches the parabola

y^{2} = 4 x,

is

HARD

JEE Advanced

IMPORTANT

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

If two tangents drawn from the point

(α, β)

to the parabola

y^{2} = 4 x

such that the slope of one tangent is double of the other, then

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 46

The tangents from the origin to the parabola

y^{2} + 4 = 4 x

are inclined at

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 47

The minimum distance between the parabolas

y^{2} - 4 x - 8 y + 40 = 0

and

x^{2} - 8 x - 4 y + 40 = 0

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 48

The equation of common tangent to the equal parabolas

y^{2} = 4 a x

and

x^{2} = 4 a y,

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 49

The length of common chord of the parabola

2 y^{2} = 3 (x + 1)

and the circle

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

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 50

The locus of the middle points of chords of a parabola which subtend a right angle at the vertex of the parabola, is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 51

The locus of a point from which tangents to a parabola are at right angles, is