Eccentricity of ellipse in which angle between the straight lines joining the foci to an extremity of minor axis is pi/2 is given by__________________

Suppose foci are S (ae,0) and S' (-ae,0) and extremity of the minor axis be P(0,b).

slope of PS = -b/ae  and  slope of PS' = b/ae

since they are perpendicular the product of their slopes must be -1.

(-b/ae)(b/ae) = -1

e² = b²/a²

Also we know for ellipse : b²/a² = 1 - e²

hence e² = 1 - e²

e = 1/root(2)