Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 11

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A variable circle is described to pass through the point $(1, 0)$ and tangent to the curve $y = \tan (\tan^{- 1} x)$ . The locus of the centre of the circle is a parabola whose:

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Important Questions on Parabola

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 12

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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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 13

Through the vertex

O

of the parabola

y^{2} = 4 a x,

two chords

O P

and

O Q

are drawn and the circles on

O P

and

O Q

as diameters intersect in

R .

If

θ_{1}, θ_{2}

and

ϕ

are the angles made with axis by the tangents at

P

and

Q

on the parabola and by

O R,

then the value of

\cot θ_{1} + \cot θ_{2}

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 14

Two parabolas have the same focus. If their directrices are the

x

axis

&

the

y

axis respectively, then the slope of their common chord is -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 16

If the distance between a tangent to the parabola

y^{2} = 4 x

and a parallel normal to the same parabola is

2 \sqrt{2},

then possible values of gradient of either of them are -

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

If

P Q

is a chord of parabola

x^{2} = 4 y

which subtends right angle at vertex. Then locus of centroid of triangle

P S Q

(

S

is focus) is a parabola whose -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 19

Identify the correct statement

(s) -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 20

For parabola

y^{2} = 4 a x

consider three points

A, B, C

lying on it. If the centroid of

∆ A B C

is

(h_{1}, k_{1}) &

centroid of triangle formed by the point of intersection of tangents at

A, B, C

has coordinates

(h_{2}, k_{2}),

then which of the following is always true -

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Beta Question Bank for Engineering: Mathematics>Chapter 18 - Parabola>EXERCISE-2>Q 21

Equation

x^{2} - 2 x - 2 y + 5 = 0

represents -