if the normal at any point P meets the major and minor axes at G and G1 and OF be the perpendicular upon this normal then show that PF.PG=b^2 and PF.PG1=a^2.

let P be (x0,y0),x²/a² + y²/b² =1,implicit diferentiation yields 2x/a²+2yy'/b²=0, y'=-(xb²)/(ya²)...equation(1),equation of normal=

(y-y0)/(x-x0)=-1/y', major axis is y=0,solve equation of normal and y=0 to get G. similarly find G1

perpendicular upon normal is given by (y/x)=y'...equation(2),solve (1) and (2) to find F