JEE MAIN - Mathematics (2021 - 27th July Morning Shift - No. 13)

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set {P, Q} is equal to :
{(4, 0), (0, 6)}
$$\{ (2 + 2\sqrt 2 ,3 - \sqrt 5 ),(2 - 2\sqrt 2 ,3 + \sqrt 5 )\} $$
$$\{ (2 + 2\sqrt 2 ,3 + \sqrt 5 ),(2 - 2\sqrt 2 ,3 - \sqrt 5 )\} $$
{($$-$$1, 5), (5, 1)}

Explanation



$$\tan \theta = - {2 \over 3}$$

Using symmetric from of line

$$P,Q:\left( {2 \pm \sqrt {13} \cos \theta ,3 \pm \sqrt {13} \sin \theta } \right)$$

$$\left( {2 \pm \sqrt {13} .\left( { - {3 \over {\sqrt {13} }}} \right),3 \pm \sqrt {13} \left( {{2 \over {\sqrt {13} }}} \right)} \right)$$

($$-$$1, 5) & (5, 1)

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