Question

Find the equation of the following ellipse. Express your answer in standard form.Enable Zoom/PanPrev

Answer 1

Answer:
`((x+3)^(2))/(4)=((y+1)^(2))/(16)`

Explanations:

The equation of an ellipse is of the form:

`((x-h)^2)/(a^2)=((y-k)^2)/(b^2)`

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

`\begin{gathered} ((x-(-3))^2)/(2^2)=((y-(-1))^2)/(4^2) \\ \\ ((x+3)^2)/(4)=((y+1)^2)/(16) \end{gathered}`