Question

if the minor axis of ellipse subtend a right angle at its focus then find the ecentricity of ellipse.



plzz answer fast.....​

Answer 1

Answer:

I think there is some misprint . This what question means (see diagram)

Now slope equals to -1 of perpendicular lines.

$\frac{b}{ ae} \times \frac{b}{ - ae} = - 1 \\ {b}^{2} = {a}^{2} {e}^{2} \\ {e}^{2} = \frac{ {b}^{2} }{ {a}^{2} }$

Now formula for eccentricity

${e}^{2} = 1 - \frac{ {b}^{2} }{ {a}^{2} } = 1 - {e}^{2} \\ 2 {e}^{2} = 1 \\ e = \frac{1}{ \sqrt{2} }$