Solve this following


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

  1. $\{(4,0),(0,6)\}$

  2. $\{(2+2 \sqrt{2}, 3-\sqrt{5}),(2-2 \sqrt{2}, 3+\sqrt{5})\}$

  3. $\{(2+2 \sqrt{2}, 3+\sqrt{5}),(2-2 \sqrt{2}, 3-\sqrt{5})\}$

  4. $\{(-1,5),(5,1)\}$

Correct Option: , 4


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

Using symmetric from of line

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

$\left(2 \pm \sqrt{13} \cdot\left(-\frac{3}{\sqrt{13}}\right), 3 \pm \sqrt{13}\left(\frac{2}{\sqrt{13}}\right)\right)$

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


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