Let d1, and d2 be the lengths of the perpendiculars drawn from the foci S and S' of the ellipse x2a2+y2b2=1 to the tangent at any point P on the ellipse.   Then, SP : S'P =

Tangent at P(acos⁡α,bsin⁡α) is xacos⁡α+ybsin⁡α=1The distance of focus s(ae,0) from this tangent isd1=|ecos⁡α−1|cos2⁡αa2+sin2⁡αb2=1−ecos⁡αcos2⁡αa2+sin2⁡αb2' *u distance of focus s'(-ae, 0) from this line is d2=1+ecos⁡αcos2⁡αa2+sin2⁡αb2or  d1d2=1−ecos⁡α1+ecos⁡αNow, SP=a−aecos⁡α and S′P=a+aecos⁡αor  SPS'P=1−ecos⁡α1+ecos⁡α=d1d2