Question

If the coordinates of a variable point P be $(acos\theta ,bsin\theta )$ where $\theta$ is a variable quantity , find the locus of P.

Answer 1

Let, $x=acos\theta$ and $y=bsin\theta$

Therefore,

=> $\frac{x}{a}=cos\theta$ ....(1)

and

$\frac{y}{b}=sin\theta$....(2)

On squaring and adding both the equation ,

we get,

$(\frac{x}{a}{)}^2+(\frac{y}{b}{)}^2=co{s}^2\theta +si{n}^2\theta$

=> $(\frac{x}{a}{)}^2+(\frac{y}{b}{)}^2=1$,

which is an ellipse.