If the normal at P on the hyperbola x2a2−y2b2=1 meets the transverse axis at G, S is a foci ande the eccentricity of the hyperbola then SG : SP is equal to

Equation of the normal at P(asec⁡ θ, btan⁡ θ) isaxsec⁡ θ+bytan⁡ θ=a2+b2 Which meets the transverse axis atGa2+b2sec⁡ θa, 0 S(ae, 0) isSG=a2+b2sec⁡θa−aeSP=easec⁡θ−ae=a[esec⁡θ−1]SGSP=a2+a2e2−1sec⁡θ−a2ea×a[esec⁡θ−1]=e2sec⁡θ−eesec⁡θ−1=e.