Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>EXERCISE ON LEVEL-II>Q 26

EASY

JEE Main/Advanced

IMPORTANT

Earn 100

If the sum of the tangents of the base angles of a triangle described on a given base be constant, show that the locus of its vertex is a parabola.

Important Questions on Parabola

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>EXERCISE ON LEVEL-II>Q 27

A circle is described whose Centre is the vertex and whose diameter is three-quarters of the length latus rectum of a parabola

y^{2} = 4 a x (a > 0)

. Prove that the common chord of the circle and parabola bisects the distance between the vertex and the focus.

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>EXERCISE ON LEVEL-II>Q 28

Find the vertex, the length of the latus rectum and the equations of the axis and tangent at the vertex of the parabola

{(x - y + 2)}^{2} = 8 \sqrt{2} (x + y - 6)

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 1

A ray of light moving parallel to the

x

-axis gets reflected from a parabolic mirror whose equation is

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

After reflection, the ray must pass through the point:

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 2

The triangle formed by the tangent to the curve

f (x) = x^{2} + b x - b

at the point

(1, 1)

and the coordinate axes, lies in the first quadrant. If its area is

2

then the value of

b

is

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 3

If a circle and a parabola intersect in

4

points then the algebraic sum of the ordinates is :

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 4

The locus of the points of trisection of the double ordinates of the parabola

y^{2} = 4 a x,

is

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 5

If the normals at two points

P

and

Q

of a parabola

y^{2} = 4 a x

intersect at a third point

R

on the curve, then the product of ordinates of

P

and

Q

is

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice I>Q 6

If the tangent at

P

on

y^{2} = 4 a x

meets the tangent at the vertex in

Q

and

S

is the focus of the parabola, then

∠ S Q P

is equal to