we know

b² = a²(1-e²)

and the equation for an ellipse is

x²/a² + y²/b² = 1

We're told the Ellipse E has equation

x²/2² + y²/3² = 1

so 9 = 4(1-e²)

4e² = -5

which you cant do, because that would be a complex number. BUT howcome you can get around this by swapping the values for a and b round. That also means that the focus has now transferred to the y axis, rather than the x, as foci as (ae,0) and now a = b?

Thanks