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.


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