Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 6

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The vertex of the locus of a point that divides a chord of slope $2$ of the parabola $y^{2} = 4 x$ internally in the ratio $1 : 2$ is

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Important Questions on Parabola

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 7

A B, A C

are tangents to a parabola

y^{2} = 4 a x

,

p_{1}, p_{2}, p_{3}

are the lengths of the perpendiculars from

A, B, C

on any tangent to the curve, then

p_{2}, p_{1}, p_{3}

are in

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 8

The mirror image of the parabola

y^{2} = 4 x

in the tangent to the parabola at the point

(1, 2)

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 9

A normal chord of the parabola subtending a right angle at the vertex makes an acute angle

θ

with the

x

-axis, then

θ =

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 10

If two normals to a parabola

y^{2} = 4 a x

intersect at right angles then the chord joining their feet passes through a fixed point whose co-ordinates are

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 11

If a parabola whose length of latus rectum is

4 a

touches both the coordinate axes then the locus of its focus is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 12

T

is a point on the tangent to a parabola

y^{2} = 4 a x

at its point

P .

T L

and

T N

are the perpendiculars on the focal radius

S P

and the directrix of the parabola respectively. Then

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 13

In the parabola,

y^{2} = 4 a x,

the locus of middle points of all chords of constant length

c

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 14

Through the vertex '

O

' of the parabola

y^{2} = 4 a x

, variable chords

O P

and

O Q

are drawn at right angles. If the variable chord

P Q

intersects the axis of

x

at

R

, then the distance

O R

is equal to