JEE Math Practice Question
Let e1 and e2 be the eccentricities of the ellipse $\frac{x^2}{b^2} + \frac{y^2}{25} = 1$ and the hyperbola $\frac{x^2}{16} - \frac{y^2}{b^2} = 1$, respectively. If b < 5 and e1e2 = 1, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :
- A.$\frac{4}{5}$
- B.$\frac{3}{5}$
- C.$\frac{\sqrt{7}}{4}$
- D.$\frac{\sqrt{3}}{2}$
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