Answer:[tex]\frac{(x+3)^{2}}{4}=\frac{(y+1)^{2}}{16}[/tex]
Explanations:
The equation of an ellipse is of the form:
[tex]\frac{(x-h)^2}{a^2}=\frac{(y-k)^2}{b^2}[/tex]
The center of the ellipse, (h, k) = (-3, -1)
The horizontal radius, a = 2
The vertical radius, b = 4
Substitute these values into the equation
[tex]\begin{gathered} \frac{(x-(-3))^2}{2^2}=\frac{(y-(-1))^2}{4^2} \\ \\ \frac{(x+3)^2}{4}=\frac{(y+1)^2}{16} \end{gathered}[/tex]
