Let us have a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ and assume the normal at P meets the transverse (horizontal) axis $AA'$ in $G$ and the conjugate (vertical) axis $BB'$ in $g$. Assume CF be perpendicular to the normal from the center.
- Find $\frac{PF \cdot PG}{CB^2}$
- Find $PF \cdot Pg$
How can I solve the question in least amount of steps? My attempt:
I first formed the equation of the normal and then I found out the points where it cuts the conjugate and transverse axis. After finding these points I used distance formula to find the distance required and convert it in the form that the question asked. But its a long method and took lot of steps
