Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 20

HARD

JEE Main

IMPORTANT

Earn 100

At a point $P$ on the parabola $y^{2} = 4 a x$ , a tangent and normal are drawn. Tangent intersects the $x$ -axis at $Q$ and normal intersects the curve at $R$ such that chord $P R$ subtends an angle of $90^{o}$ at its vertex. Then

50% studentsanswered this correctly

Important Questions on Parabola

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 21

Let

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

be a parabola, then

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 1

If three parabolas touch all the lines

x = 0, y = 0

and

x + y = 2

, then the maximum area of the triangle formed by joining their foci is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 2

If

2 x + 3 y = α, x - y = β

and

k x + 15 y = r

are

3

concurrent normals of parabola

y^{2} = λ x

, then the value of

k

is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 3

Let

(2, 3)

be the focus of a parabola and

x + y = 0

and

x - y = 0

be its two tangents. Then equation of its directrix will be

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 4

In the following figure, $A S = 4$ units and $S P = 9$ units. The value of $S Z$ is

Question Image

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 5

Let

T P

and

T Q

be any two tangents to a parabola and the tangent at a third point

R

cuts them in

P^{'}

and

Q^{'}

. Then the value of

\frac{T P^{'}}{T P} + \frac{T Q^{'}}{T Q}

must be

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 6

The distance of two points

P

and

Q

on the parabola

y^{2} = 4 a x

from the focus

S

are

3

units and

12

units, respectively. The distance of the point of intersection of the tangents at

P

and

Q

from the focus

S

is

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 7

A parabola having directrix

x + y + 2 = 0

touches a line

2 x + y - 5 = 0

at

(2, 1)

. Then the semi-latus rectum of the parabola is