Question

By eliminating $\theta$ from $x=a{\cos }^2\theta ,y=a{\sin }^2\theta$ the expression is

Answer 1

We have,

$x=a{\cos }^2\theta$ ……. (1)

$y=a{\sin }^2\theta$ …….. (2)

On adding both equations, we get

$x+y=a{\cos }^2\theta +a{\sin }^2\theta$

$x+y=a({\cos }^2\theta +{\sin }^2\theta )$

We know that

${\cos }^2\theta +{\sin }^2\theta =1$

Therefore,

$x+y=a$

Hence, this is the answer.