The graph represents a vertical ellipse with centre (h,k)=(0,-2)
Length of major axis, 2a =6, that gives, a=3
And length of minor axis, 2b =2, that gives b=1 .
The equation of vertical ellipse is
[tex] \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1 [/tex]
Substituting the values of h,k,a and b, we will get
[tex] \frac{(x)^2}{1}+\frac{(y+2)^2}{9}=1 [/tex]
