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

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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

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Important Questions on Parabola

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 15

From the focus of the parabola,

y^{2} = 8 x

as centre, a circle is described so that a common chord of the curves is equidistant from the vertex & focus of the parabola. Find the equation of the circle.

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 16

If from the vertex of a parabola

y^{2} = 4 a x

, a pair of chords be drawn at right angles to one another and with these chords as adjacent sides a rectangle be made, locus of the further angle of the rectangle is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 21

The parabola whose axis is parallel to the

y

-axis and which passes through the points

(0, 4), (1, 9)

and

(- 2, 6)

, also passes through

(2, α)

then the value of

α

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 22

Through the vertex

O

of the parabola

y^{2} = 8 x

, a perpendicular is drawn to any tangent meeting it at

P

and the parabola at

Q,

then the value of

O P \cdot O Q

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 23

The centre of the circle which passes through the focus of the parabola

x^{2} = 4 y

& touches it at the point

(6, 9)

is

(α, β)

then

|α - β|

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 26

If three normal are drawn through

(c, 0)

to

y^{2} = 4 x

and two of which of perpendicular then the value of

c

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 27

Common tangents are drawn to the parabola

y^{2} = 4 x

and the ellipse

3 x^{2} + 8 y^{2} = 48

touching the parabola at

A & B

and the ellipse at

C & D

, then the area of the quadrilateral

A B C D

is

λ \sqrt{2}

then

λ

is equal to

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 28

Let tangent at point

A B

and vertex

(V)

of parabola is

x - 2 y + 1 = 0, 3 x + y + 4 = 0

and

y = x

respectively. If focus of parabola is

(\frac{a}{7}, \frac{b}{7})

then find the value of

(a + 5 b) .