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

HARD

JEE Advanced

IMPORTANT

Earn 100

Radius of the circle that passes through origin and touches the parabola $y^{2} = 4 a x$ at the point $(a, 2 a)$ is

50% studentsanswered this correctly

Important Questions on Parabola

EASY

JEE Advanced

IMPORTANT

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

A line

L

passing through the focus of the parabola

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

and intersects the parabola in two distinct points. If

m

is the slope of the line

L,

then

m

can take values in the interval

HARD

JEE Advanced

IMPORTANT

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

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

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