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Parabola question

2015 · Shift 1 · Q24

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PYQ Library
JEE Advanced
Mathematics
Parabola
2015 · Shift 1 · Q24

Parabola question

2015 · Shift 1 · Q24

JEE AdvancedMathematicsParabolaMultiple correct+4 / −1

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

?

A
$\left( {4,2\sqrt 2 } \right)$
B
$\left( {9,3\sqrt 2 } \right)$
C
$\left( {{1 \over 4},{1 \over {\sqrt 2 }}} \right)$
D
$\left( {1,\sqrt 2 } \right)$

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