The tangent at to the ellipse

cuts the y-axis at Q. The normal at P is parallel to the line joining Q to one focus S'. if S is the other focus, show that PS is parallel to the y-axis.

S'(-ae,0) and S(ae,0)

so gradient of QS'

this means

that would make ae=

but in order for PS to be vertical, ae needs to be

i.e. e=