Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 17

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The locus of the centroid of a triangle formed by a tangent to the parabola $y^{2} = 36 x$ with the coordinate axes, is

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Important Questions on Parabola

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 18

P C

is the normal at

P

to the parabola

y^{2} = 4 a x, C

being on the axis.

C P

is produced outwards to

Q

so that

P Q = C P

. The locus of

Q

is a parabola that has focus

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Chapterwise/Topicwise Daily Practice Problems (DPP) Coor.dinate Geometry JEE Main & Advanced>Chapter 5 - Parabola>DPP>Q 19

If the parabolas

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

and

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

do not have a common normal other than the axis of parabola, then

k \in

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

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

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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

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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

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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

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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

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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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