Find an equation for the ellipse shown in the figure Solutio

Find an equation for the ellipse shown in the figure.

Solution

Centre ,(h,k)=(-2,1)

Length of major axis ,2a=sqrt((-6-2)²+(1-1)²)=8

a=4

Length of minor axis ,2b=sqrt((-2+2)²+(3+1)²)=4

b=2

Required equation is

(x+2)²/16 +(y-1)²/4=1