Let each of the two ellipses E₁:x²/a²+y²/b²=1 (ab) and E₂:x²/A²+y²/B²=1 (A

Question

Let each of the two ellipses $$E_1:\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1\;(a>b)$$ and $$E_2:\dfrac{x^2}{A^2}+\dfrac{y^2}{B^2}=1\;(A<B)$$ have eccentricity $$\dfrac{4}{5}$$. Let the lengths of the latus recta of $$E_1$$ and $$E_2$$ be $$l_1$$ and $$l_2$$, respectively, such that $$2l_1^2=9l_2$$.
If the distance between the foci of $$E_1$$ is $$8$$, then the distance between the foci of $$E_2$$ is

Accepted Answer

D. $$\dfrac{32}{5}$$

Answer

A. $$\dfrac{16}{5}$$

Answer

B. $$\dfrac{96}{5}$$

Answer

C. $$\dfrac{8}{5}$$

Answer & step-by-step solution

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