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

`((x-h)^2)/(a^2)+((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} ((x--2)^2)/(2^2)+((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`