Question

If $x=a(\sec \theta +\tan \theta ),y=a(\sec \theta -\tan \theta )$, eliminate $\theta$.

Answer 1

Given,

$x=a(\sec \theta +\tan \theta )$, $y=a(\sec \theta -\tan \theta )$.

or, $\frac{x}{a}=(\sec \theta +\tan \theta )$......(1) and $\frac{y}{a}=(\sec \theta -\tan \theta )$.......(2).

Now multiplying (1) and (2) we get,

$\frac{xy}{a^2}=({\sec }^2\theta -{\tan }^2\theta )$

or, $xy=a^2$. [ Since ${\sec }^2\theta -{\tan }^2\theta =1$]