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 the

\Delta OPQ

3\sqrt{2}

, then which of the following is (are) the coordinates of

P

? a.

(4, 2\sqrt{2})

(9, 3\sqrt{2})

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

(1, \sqrt{2})