Question

Eliminate $\theta$, if:
$x=p\sec \theta ,y=q\tan \theta$

Answer 1

$x=p\sec \theta$
$y=q\tan \theta$
$\therefore \sec \theta =\frac{x}{p}$
$\therefore \tan \theta =\frac{y}{q}$
$\therefore {\sec }^2\theta =\frac{x^2}{p^2}$ ....... (1)
$\therefore {\tan }^2\theta =\frac{y^2}{q^2}$ ....... (2)

we know that ${\sec }^2\theta -{\tan }^2\theta =1$

$\frac{x^2}{p^2}-\frac{y^2}{q^2}=1$