Let be the vertex and be any point on the parabola

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

O

be the vertex and

Q

be any point on the parabola

x^2=8y

. If the point

P

divides the line segment

OQ

internally in the ratio

1:3

, then the locus of

P

is (1)

x^2=y

(2)

y^2=x

(3)

y^2=2x

(4)

x^2=2y