Question

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 

(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)}

Answer 1

tan\(\theta\) = \(-\frac{2}{3}\)

3 Using symmetric from of line P,Q : (2\(\pm\) \(\sqrt{13}\) cos\(\theta\), 3\(\pm\)\(\sqrt{13}\) sin\(\theta\))

(–1, 5) & (5, 1)