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

The distance of foci = c

Then,

c = 6

To this question, a = 8

As a^2 = b^2 + c^2

Then us will have:

8^2 = 6^2 + c^2

64 = 36 + c^2

64 - 36 = c^2

c^2 = 28

c = √ (28)

c = √ (7*4)

c = 2√ (7)

The equation to this question is:

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

Then,

y^2 / 64 + x^2/36 = 1