Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 8

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If $M$ is the foot of the perpendicular from a point $P$ of a parabola $y^{2} = 4 a x$ to its directrix and $S P M$ is an equilateral triangle, where $S$ is the focus, then $S M$ is equal to -

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Important Questions on Parabola

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 9

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 distance

O R

:

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 10

The triangle

P Q R

of area

A

is inscribed in the parabola

y^{2} = 4 a x

such that the vertex

P

lies at the vertex of the parabola and the base

Q R

is a focal chord. The modulus of the difference of the ordinates of the points

Q

and

R

is

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 11

Point

P

lies on

y^{2} = 4 a x & N

is foot of perpendicular from

P

on its axis. A straight line is drawn parallel to the axis to bisect

N P

and meets the curve in

Q

.

N Q

meets the tangent at the vertex in a point

T

such that

A T = k N P,

then the value of

k

is : (where

A

is the vertex)

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 12

The tangents to the parabola

x = y^{2} + c

from origin are perpendicular then

c

is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 13

The locus of a point such that two tangents drawn from it to the parabola

y^{2} = 4 a x

are such that the slope of one is double the other is -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 14

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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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 15

The equation of the circle drawn with the focus of the parabola

(x - 1)^{2} - 8 y = 0

as its centre and touching the parabola at its vertex is :

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 16

Length of the normal chord of parabola

y^{2} = 4 x

which makes an angle of

\frac{π}{4}

with the axis of

x

is