Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 42

HARD

JEE Main/Advance

IMPORTANT

Earn 100

The distance between the focus and directrix of the conic $(\sqrt{3} x - y)^{2} = 48 (x + \sqrt{3} y)$ is

62.5% studentsanswered this correctly

Important Questions on Parabola

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 43

If one end of a focal chord of the parabola

y^{2} = 4 x

is

(1, 2)

, the other end doesn't lie on

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 44

The locus of point of trisection of the double ordinates of the parabola,

y^{2} = 4 x

is

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 45

The latus rectum of the parabola

y^{2} = 4 a x

, whose focal chord is

P S Q,

such that

S P = 3

and

S Q = 2

is given by

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 46

Identify following statements for true/false (T / F) in order

S 1 :

The circles on focal radii of a parabola as diameter touch the tangent at the vertex

S 2 :

The circles on focal radii of a parabola as diameter touch the axis

S 3 :

A circle described on any focal chord of the parabola as its diameter will touch the directrix of the parabola

S 4 :

A circle described on any focal chord of the parabola as its diameter will touch the axis of the parabola

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 47

The length of the chord

y = \sqrt{3} x - 2 \sqrt{3}

intercepted by the parabola

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

is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 48

If

y = 2 x - 3

is a tangent to the parabola

y^{2} = 4 a (x - \frac{1}{3})

, then

a

is equal to, where

a \neq 0

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 49

An equation of a tangent common to the parabolas

y^{2} = 4 x

and

x^{2} = 4 y

is

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 50

Equation of a tangent to the parabola

y^{2} = 12 x

which make an angle of

45^{°}

with line

y = 3 x + 77

is