The foci of an ellipse are S, S' and P is any point on the curve. The normal at P meets SS' at G. Prove the

whereeis the eccentricity of the ellipse.

I let P(s,t)

the equation of the ellipse

where

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

gradient of normal at P=

equation PG

when y=0

then

PS.PS'=

Now my problem is here, i cannot find a square root for this expression.

Thanks