This is a vertical ellipse since it's taller than it is wider. That means that y is the transversal axis, aka the major axis. The formula for this type of ellipse is[tex] \frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1 [/tex]
where h and k are the center of the ellipse and a is the number of units from the center along the minor axis to the outside of the ellipse and b is the number of units from the center along the major axis to the outside of the ellipse. Here, our h and k are, respectively, (0, -3), a = 1 and b = sqrt(3). Fitting those values into our formula we have the equation as
[tex] \frac{x^2}{\sqrt{3}}+\frac{(y+3)^2}{1} =1 [/tex].
That's your answer!
