A geometry problem by ashwin korade

Geometry Level 3

If the foci of the ellipse \(\frac{x^2}{16} + \frac{y^2}{b^2} = 1\) and the hyperbola, \(\frac{x^2}{144} - \frac{y^2}{81} = \frac{1}{25}\) coincide then find the value of \(b^2\).

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