If any tangent to the hyperbola with centre

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

If any tangent to the hyperbola

\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1

with centre

C

, meets its director circle in

P

and

Q

, show that

CP

and

CQ

are conjugate semi-diameters of the hyperbola.