Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passe…

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 :

Accepted Answer

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

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)

Solutions · 1