# JEE-Advanced 2015 (13/40)

**Geometry**Level 3

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 triangle \(\Delta OPQ\) is \(3\sqrt{2}\), then which of the following is(are) the coordinates of \(P\) ?

\[\begin{array}{} (1) \, (4,2\sqrt{2}) \quad \quad \quad \quad & (2) \, (9,3\sqrt{2}) \\ (3) \, (\frac{1}{4}, \frac{1}{\sqrt{2}} ) & (4) \, (1,\sqrt{2}) \end{array}\]

**Note :**

Submit your answer as the increasing order of the serial numbers of all the correct options.

For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.