Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 9

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

Find the equations of the tangents of the parabola $y^{2} = 12 x$ , which passes through the point $(2, 5) .$

Important Questions on Parabola

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 10

Show that the normals at the points

(4 a, 4 a)

&

at the upper end of the latus rectum of the parabola

y^{2} = 4 a x

intersect on the same parabola.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 11

Prove that the locus of the middle point of portion of a normal to

y^{2} = 4 a x

intercepted between the curve & the axis is another parabola. Find the vertex & the latus rectum of the second parabola.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 12

P & Q

are the points of contact of the tangents drawn from the point

T

to the parabola

y^{2} = 4 a x

. If

P Q

be the normal to the parabola at

P

then prove that

T P

is bisected by the directrix.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 13

The normal at a point

P

to the parabola

y^{2} = 4 a x

meets its axis at

G

.

Q

is another point on the parabola such that

Q G

is perpendicular to the axis of the parabola. Prove that

Q G^{2} - P G^{2} =

constant.

EASY

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 14

Three normals to

y^{2} = 4 x

pass through the point

(15, 12) .

Show that one of the normals is given by

y = x - 3

&

find the equations of the others.

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 15

Find the equation of the parabola whose focus is

(- 3, 0)

and the directrix is

x + 5 = 0

.

HARD

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 16

Find the vertex, axis, focus, directrix, latus rectum of the parabola

x^{2} + 2 y - 3 x + 5 = 0 .

MEDIUM

JEE Main/Advance

IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-4>Q 17

Prove that the locus of the middle points of all tangents drawn from points on the directrix to the parabola

y^{2} = 4 a x

is

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

.