Question

Find an equation of the ellipse that has center (-2;-2), a major axis of length 12, and endpoint of minor axis (0, -2).

Answer 1

The Solution:

The formula for the equation of an ellipse is

$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$

In this case,

$\begin{gathered} h=-2 \\ k=-2 \\ a=2 \\ b=6 \end{gathered}$

Substituting the above values in the formula above, we get

$\begin{gathered} \frac{(x--2)^2}{2^2}+\frac{(y--2)^2}{6^2}=1 \\ \\ \frac{(x+2)^2}{4^{}}+\frac{(y+2)^2}{36^{}}=1 \end{gathered}$

Therefore, the equation of the ellipse is

$\frac{(x+2)^2}{4^{}}+\frac{(y+2)^2}{36^{}}=1$