Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 24

HARD

JEE Main/Advance

IMPORTANT

Earn 100

Find the locus of the mid-point of the focal chord of the parabola $y^{2} = 4 x$ .

Important Questions on Parabola

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 25

Find the equation of all possible normals to the parabola

x^{2} = 4 y

drawn from point

(1, 2)

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 26

If

a x + b y = 1

is a normal to the parabola

y^{2} = 4 P x,

then prove that

P a^{3} + 2 a P b^{2} = b^{2}

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 27

Find the equation of normal to the parabola

x^{2} = 4 y

at

(6, 9) .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 28

The normal at the point

P (a p^{2}, 2 a p)

meets the parabola

y^{2} = 4 a x

again at

Q (a q^{2}, 2 a q)

such that the lines joining the origin to

P

and

Q

are at right angle. Then prove that

p^{2} = 2

.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 31

Find the equation of a circle touching the parabola

y^{2} = 8 x

at

(2, 4)

and passing through

(0, 4) .

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 32

The equation of the parabola whose focus is

(- 3, 0)

and the directrix is

x + 5 = 0

is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 33

If

(2, 0)

is the vertex and

Y

-axis is the directrix of a parabola, then its focus is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 34

Length of the latus rectum of the parabola

25 [{(x - 2)}^{2} + {(y - 3)}^{2}] = {(3 x - 4 y + 7)}^{2}

is