Ellipse and Hyperbola Eccentricities (Jee Mains)

Ellipse

Hard

Ellipse and Hyperbola Eccentricities

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 :

SELECT ONE OPTION

Ask about this question