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

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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

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Important Questions on Parabola

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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

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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

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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

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JEE Main

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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

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 8

Let

A, B

and

C

be three distinct points on

y^{2} = 8 x

such that normals at these points are concurrent at

P

. The slope of

A B

is

2

and abscissa of centroid of

△ A B C

is

\frac{4}{3}

. Which of the following is (are) correct?

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 9

If $P Q$ and $R S$ are normal chords of the parabola $y^{2} = 8 x$ at $P & R$ , respectively, and the points $P, Q, R$ and $S$ are concyclic, then

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JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 10

Tangents are drawn from

P (- 2, 0)

to

y^{2} = 8 x

. Radius of circle(s) that would touch these tangents and the corresponding chord of contact can be equal to

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JEE Main

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 11

Given a parabola

y^{2} = 4 a x

and the points

A (a t^{2}, 2 a t), B (a t^{- 2}, - 2 a t^{- 1}), C (\frac{4 a}{t^{2}}, \frac{4 a}{t})

and

D (a {(t + \frac{2}{t})}^{2}, - 2 a (t + \frac{2}{t}))

, choose all the correct alternatives.