What is the area of a square inscribed in an ellipse 16x² + 9y² = 144?

This is a harder one. I can only work up to the value of a and b but do not know how to find the area of square.

16x²/144 + 9y²/144 = 1

x²/9 + y²/16 = 1

So I know a²=9, therefore a=3 and b²=16 and b=4.

Because a < b, I know this is a vertical ellipse.

The next step is to find the area of a square inscribed in the ellipse. But how?

Thanks.