Question

Eliminate $\theta$ from the following equations:

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

Answer 1

We have,

$x=a(\sec \theta +\tan \theta )$ ……. (1)

$y=b(\sec \theta -\tan \theta )$ ……. (2)

From equation (1) and (2), we get

$xy=ab(\sec \theta +\tan \theta )(\sec \theta -\tan \theta )$

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

We know that

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

Therefore,

$xy=ab\times 1$

$xy=ab$

Hence, this is the answer.