JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
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 \(O C\) is perpendicular to both the line segments \(C P\) and \(C Q\), then the set \(\{\mathrm{P}, \mathrm{Q}\}\) is equal to:
- A \(\{(-1,5),(5,1)\}\)
- B \(\{(2+2 \sqrt{2}, 3-\sqrt{5}),(2-2 \sqrt{2}, 3+\sqrt{5})\}\)
- C \(\{(2+2 \sqrt{2}, 3+\sqrt{5}),(2-2 \sqrt{2}, 3-\sqrt{5})\}\)
- D \(\{(4,0),(0,6)\}\)
Answer & Solution
Correct Answer
(A) \(\{(-1,5),(5,1)\}\)
Step-by-step Solution
Detailed explanation
\(\tan \theta=-\frac{2}{3}\) Using symetric from of line \(P, Q:(2 \pm \sqrt{13} \cos \theta, 3 \pm \sqrt{13} \sin \theta)\) \(\left(2 \pm \sqrt{13} \cdot\left(-\frac{3}{\sqrt{3}}\right), 3 \pm \sqrt{3}\left(\frac{2}{\sqrt{13}}\right)\right)\)a \((-1,5)\, \&\,(5,1)\)
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