A geometry problem by Vidit Mathur

Geometry Level pending

If the focii of the ellipse \frac { { x }^{ 2 } }{ 25 } + \frac { { y }^{ 2 } }{ { b }^{ 2 } } =1 and the hyperbola \frac { { x }^{ 2 } }{ 144 } -\frac { { y }^{ 2 } }{ 81 } =\frac { 1 }{ 25 } coincide then the value of { b }^{ 2 } is :

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