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.