Question

Find the equation of the ellipse with the following properties.

The ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8) and (0, -8).

Answer 1

since the foci are on the y- axis, this is an ellipse elongated vertically... with the center at the origin... the distance from the center to the foci is 6 so c=6. because of the vertices, a=8.

so in the relation c^2 = a^2 - b^2 ---> b^2 = a^2 - c^2

the standard form for the ellipse is :

x^2/b^2 + y^2/a^2 = 1

plug those values in to get the equation you require.

Answer 2

thank you!