Let the ellipse E_1: (x^2)/(a^2) + (y^2)/(b^2) = 1, a b and E_2: (x^2)/(A^2) + (y^2)/(B^…

Question

Let the ellipse $E_1: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, $a > b$ and $E_2: \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$, $A < B$ have same eccentricity $\frac{1}{\sqrt{3}}$

Accepted Answer

$\begin{gathered} (x,y)\equiv (\frac{\sqrt{6}}{\sqrt{5}},\frac{6}{\sqrt{5}}),(\frac{-\sqrt{6}}{\sqrt{5}},\frac{6}{\sqrt{5}}),(\frac{\sqrt{6}}{\sqrt{5}},\frac{-6}{\sqrt{5}}),(\frac{-\sqrt{6}}{\sqrt{5}},\frac{-6}{\sqrt{5}}) \ = \ \frac{24\sqrt{6}}{5} \end{gathered}$

Solutions · 1