If the ellipse x^2/a^2 + y^2/b^2 = 1 (where a > b) passes through point (4√2/5, 3) and its eccentricity is 1/4 then the value of a^2 + b^2

Question

If the ellipse \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) (where a > b) passes through point \(\left(4\sqrt{\frac25},3\right)\) and its eccentricity is \(\frac14 \) then the value of a² + b² is equal to ___.

Answer 1

\(\left(4\sqrt{\frac25},3\right)\) lies on ellipse