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The general equation of a horizontal ellipse is
(x-h)2/a2 + (y-k)2/b2 = 1, at center (h,k) while a = semi-major axis, b = semi-minor axis. These are related through the distance of the focus from the center,c. a2 = b2 + c2.
If you draw the points on a coordinate plane, the center of the ellipse is at (0,0), so h and k equals 0. Then, the minor axis (2b) spans from 8 to -8 of the y-axis. This is equal to 16 units. Hence,
2b = 16 b = 8 b^2 = 64
The distance between the two foci is 2c. Thus,
2c = 12 c = 6 c^2 = 36
Then, a2 = 64 + 36 = 100. Substituting to the general equation:
