If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies:

Equation of the ellipse is x2a2+y2b2=1 One end of the latursectum is Lae,b2aEquation of the normal at the point L isa2xx1−b2yy1=a2−b2a2xae−b2yb2/a=a2e2 The above normal is passing through the point (0,-b) , one end of the minor axis ⇒0+ab=a2e2⇒ba=e2⇒b2a2=e4⇒1−e2=e4⇒e4+e2−1=0