Question

Write the parametric equation of ellipse $\frac{(x-3{)}^2}{25}+\frac{(y+2{)}^2}{16}=1$.

Answer 1

Given equation of ellipse is $\frac{(x-3{)}^2}{25}+\frac{(y+2{)}^2}{16}=1$

let $X=x-3,Y=y+2$

$⟹\frac{X^2}{5^2}+\frac{Y^2}{4^2}=1$

This is in the form of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

$⟹a=5,b=4$

The parametric equation of this ellipse is $x=a\cos \theta ,y=b\sin \theta$

$⟹X=5\cos \theta ,Y=4\sin \theta$

$⟹x-3=5\cos \theta ,y+2=4\sin \theta$

$⟹x=3+5\cos \theta ,y=-2+4\sin \theta$