If the foci of the ellipse 16x2+b2y2=1 and the hyperbola 144x2−81y2=251 coincide, then find the value of b2

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Question

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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Noah Discussed

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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Question Text

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}