If y^2 / b^2 = 1 - x^2 / (4a^2)

Then (x^2/a^2) - (1 - x^2 / (4a^2)) = 1

This leads to x^2 = (8/5)a^2

Similarly, one can determine that y^2 = (3/5)b^2

From the given points, we have x^2 = 72/5 and y^2 = 27/5

That seem to be enough to find a and b.

Let's see what you get.