Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 33

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$P$ is a point on the parabola $y^{2} = 4 x$ where abscissa and ordinate are equal. Equation of a circle passing through the focus and touching the parabola at $P$ 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 34

Locus of the centre of the circle passing through the vertex and the mid-points of perpendicular chords from the vertex of the parabola

y^{2} = 4 a x

is.

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 35

The equation

3 x^{2} + 4 y^{2} - 18 x + 16 y + 43 = c

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-2>Q 36

Two confocal parabola intersect at

A

and

B

. If their axis are parallel to

x

-axis and

y

-axis respectively, then slope of chord

A B

can be :

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-3>Q 1

The tangent

P T

and the normal

P N

to the parabola

y^{2} = 4 a x

at a point

P

on it meet its axis at points

T

and

N

respectively. The locus of the centroid of triangle

P T N

is a parabola whose

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-3>Q 3

Let

A

and

B

be two distinct points on the parabola

y^{2} = 4 x

. If the axis of the parabola touches a circle of radius

r

having

A B

as its diameter, then the slope of the line joining

A

and

B

can be

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-3>Q 5

Let

L

be normal to the parabola

y^{2} = 4 x

. If

L

passes through the point

(9, 6)

, then

L

is given by

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-3>Q 9

Let the curve

C

be the mirror image of the parabola

y^{2} = 4 x

with respect to the line

x + y + 4 = 0

. If

A

and

B

are the points of intersection of

C

with the line

y = - 5

, then the distance between

A

and

B

is

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Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-3>Q 10

If the normals of the parabola

y^{2} = 4 x

drawn at the end points of its latus rectum are tangents to the circle

(x - 3)^{2} + (y + 2)^{2} = r^{2}

, then the value of

r^{2}

is