Centered at the origin means (h,k) =(0,0)
Length of major axis, 2a = 20
That gives, a =10
Length of minor axis, 2b =18
That gives, b=9
And since focii is on the y axis, so its a vertical ellipse of the form
[tex] \frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} =1
[/tex]
Substituting the values of a and b, we will get
[tex] \frac{x^2}{81}+\frac{y^2}{100}=1 [/tex]
