Let and be distinct points on the parabola such that a circle with as diameter passes…

MATHEMATICS · Multi correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

P

and

Q

be distinct points on the parabola

y^2=2x

such that a circle with

PQ

as diameter passes through the vertex

O

of the parabola. If

P

lies in the first quadrant and the area of

\triangle OPQ

3\sqrt{2}

, then which of the following are the coordinates of

P

? (1)

(4,2\sqrt{2})

(2)

(9,3\sqrt{2})

(3)

\left(\frac{1}{4},\frac{1}{\sqrt{2}}\right)

(4)

(1,\sqrt{2})