Distance Between Foci of Ellipses (Jee Mains)

Ellipse

Hard

Distance Between Foci of Ellipses

Let each of the two ellipses ${E_1}:\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1,(a > b)$ and ${E_2}:\frac{{{x^2}}}{{{A^2}}} + \frac{{{y^2}}}{{{B^2}}} = 1$ , (A < B) have eccentricity $\frac{4}{5}$ . Let the lengths of the latus rectum of E₁ and E₂ be ℓ₁ and ℓ₂, respectively, such that $2\ell _1^2 = 9{\ell _2}$ . If the distance between the foci of E₁ is 8, then the distance between the foci of E₂ is

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Ellipse

Hard

Distance Between Foci of Ellipses

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