Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 13

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Let $O$ be the vertex and $Q$ be any point on the parabola $x^{2} = 8 y .$ If the point $P$ divides the line segment $O Q$ internally in the ratio $1 : 3,$ then the locus of $P$ is

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Important Questions on Parabola

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IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 14

The shortest distance between the line

y - x = 1

and the curve

x = y^{2}

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 15

If two tangents drawn from a point

P

to the parabola

y^{2} = 4 x

are at right angles, then the locus of

P

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 16

A parabola has the origin as its focus and the line

x = 2

as the directrix. Then, the vertex of the parabola is at

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 17

The equation of a tangent to the parabola

y^{2} = 8 x

is

y = x + 2 .

The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 18

The locus of the vertices of the family of parabolas

y = \frac{a^{3} x^{2}}{3} + \frac{a^{2} x}{2} - 2 a

is

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 19

Let

P

be the point

(1, 0)

and

Q

be the point on

y^{2} = 8 x .

The locus of midpoint of

P Q

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 20

A circle touches

X

-axis and also touches the circle with centre at

(0, 3)

and radius

2 .

The locus of the centre of the circle is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Entrances Gallery>Q 21

If

a \neq 0

and the line

2 b x + 3 c y + 4 d = 0

passes through the points of intersection of the parabolas

y^{2} = 4 a x

and

x^{2} = 4 a y,

then