Answer:[tex]\frac{(x+4)^{2}}{81}+\frac{(y-4)^{2}}{4}=1[/tex]Explanation:
The center of the ellipse, (h, k) = (-4, 4)
The length of the major axis = 18
The length of the semi-major axis, a = 18/2 = 9
The length of the minor axis = 4
The length of the semi minor axis, b = 4/2 = 2
The equation of the ellipse is calculated as shown below
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]
Substitute h = -4, k = 4, a = 9, and b = 2 into the equation
[tex]\begin{gathered} \frac{(x-(-4))^2}{9^2}+\frac{(y-4)^2}{2^2}=1 \\ \\ \frac{(x+4)^2}{81}+\frac{(y-4)^2}{4}=1 \end{gathered}[/tex]
Therefore, the equation of the ellipse is:
[tex]\frac{(x+4)^{2}}{81}+\frac{(y-4)^{2}}{4}=1[/tex]
