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

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Latus rectum of the parabola whose focus is $(3, 4)$ and whose tangent at vertex has the equation $x + y = 7 + 5 \sqrt{2}$ is -

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Important Questions on Parabola

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 2

Directrix of a parabola is

x + y = 2

. If it's focus is origin, then latus rectum of the parabola is equal to -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 4

Let

C

be a circle and

L

a line on the same plane such that

C

and

L

do not intersect. Let

P

be a moving point such that the circle drawn with centre at

P

to touch

L

also touches

C

. Then the locus of

P

is -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 5

If

(t^{2}, 2 t)

is one end of a focal chord of the parabola

y^{2} = 4 x

then the length of the focal chord will be-

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 6

From the focus of the parabola $y^{2} = 8 x$ as a centre, a circle is described so that the common chord of the curves is equidistant from the vertex and focus of the parabola. The equation ofthe circle is.

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-1>Q 7

The point of intersection of the curves whose parametric equations are

x = t^{2} + 1, y = 2 t

and

x = 2 s, y = \frac{2}{s}

is given by -

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

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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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