An ellipse has its center at the origin and its minor axis is along the x-axis. If the distance between its foci is equal to the length of its minor axis and the length of its latus rectum is 4, then which of the following points lies on the ellipse?$$(2,2\sqrt2)/(2,\sqrt2)/(\sqrt2,2\sqrt2)/(2\sqrt2,2)$$
My attempt: Let $a,b, e$ be the length of minor axis, length of major axis and eccentricity, respectively. So, $2be=2a\implies a=be$. Also, $\frac{2a^2}{b}=4\implies\frac{b^2e^2}{b}=2$. Don't know how to proceed next.
Best Answer
Hint:
Use the fact that $$e=\sqrt{1-\frac{a^2}{b^2}} $$
Since $a=be$, $$e=\sqrt{1-e^2} \implies e=\frac{1}{\sqrt 2}$$
Now use this value to get $a$ and $b$, and find which point satisfies the equation of the ellipse.