Let P be any point on the directrix of an ellipse of eccentricity e. S be the corresponding focus and C the centre of the ellipse. The line PC meets the ellipse at A. the angle between PS and tangent at A is α , then α  is not equal to

Let the ellipse be x2a2+y2b2=1  and let A≡(acosθ,bsinθ) Equation of AC will be y=batanθx. Solving with x=ae, we get P(ae,betanθ) Slope of the tangent at A is −batanθ Slope of PS=betanθae−ae=btanθa(1−e2)                                          =abtanθ                              So α=π2.