If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is $90^{\circ}$, then it eccentricity is

Question

Aicharya · Accepted Answer

Apply pythagoras theorem, in $\Delta A S_1 S_2$ $\left(S_1 A\right)^2+\left(A S_2\right)^2=\left(S_1 S_2\right)^2$ $a^2+a^2=(2 a e)^2$ $\Rightarrow \quad 2 a^2=4 a^2 e^2$ $\therefore \quad e=\frac{1}{\sqrt{2}}$

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse…

Solution