Question

The coordinate of P satisfy $x=a\cos \theta ,y=b\sin \theta .$ Find the equation of the locus of P.

Answer 1

$x=a\cos \theta ,y=b\sin \theta$

$⟹\frac{x}{a}=\cos \theta ,\frac{y}{b}=\sin \theta$

$(\frac{x}{a}{)}^2+(\frac{y}{b})={\cos }^2\theta +{\sin }^2\theta =1$

The locus of $P$ is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$