(2) The equation can be written: x²/a²+y²/b²=1.
Plug in the given points and we get two equations:
9/a²+12/b²=1, 16a²+80/(9b²)=1.
From these: a²=9b²/(b²-12) and a²=144b²/(9b²-80).
Therefore 9b²/(b²-12)=144b²/(9b²-80), 1/(b²-12)=16/(9b²-80),
Cross-multiplying: 9b²-80=16b²-192, 7b²=112, b²=16, b=4.
So a²=9b²/(b²-12)=144/4=36, a=6.
The equation of the ellipse is x²/36+y²/16=1.
This can also be written: 16x²+36y²=576.