Question

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 $Q$, then:

• A. $CP$ and $CQ$ are perpendicular to each other.
• B. $CP$ and $CQ$ are conjugate semi-diameters of the hyperbola.
• C. $CP$ and $CQ$ are not conjugate semi-diameters of the hyperbola.
• D. None of the above

Answer 1

The correct option is B $CP$ and $CQ$ are conjugate semi-diameters of the hyperbola.