JEE-Advanced 2015 (13/40)

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 $P$ ?

$\begin{array}{c} (1) \, (4,2\sqrt{2}) \quad \quad \quad \quad & (2) \, (9,3\sqrt{2}) \\ (3) \, (\frac{1}{4}, \frac{1}{\sqrt{2}} ) & (4) \, (1,\sqrt{2}) \end{array}$
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.