Let \( P \) and \( Q \) be distinct points on the parabola \( y^{2}=2 x \) such that a circle wi... VIDEO
Let \( P \) and \( Q \) be distinct points on the parabola \( y^{2}=2 x \) such that a circle with \( P Q \) as diameter passes through the vertex \( O \) of the parabola. If \( P \) lies in the first quadrant and the area of the \( \triangle O P Q \) is \( 3 \sqrt{2} \), then which of the following is (are) the coordinates of \( P \) ?
(a) \( (4,2 \sqrt{2}) \)
(b) \( (9,3 \sqrt{2}) \)
(c) \( \left(\frac{1}{4}, \frac{1}{\sqrt{2}}\right) \)
(d) \( (1, \sqrt{2}) \)
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