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

Question

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

Infinity Learn · Accepted Answer

Let the ellipse be $$x2a2+y2b2=1$$      and let A≡(acos$$θ,bsinθ$$)     Equation of AC will be $$y=batan$$θx.     Solving with $$x=ae$$,     we get $$P(ae$$,betanθ$$)$$     Slope of the tangent at A is −batanθ     Slope of $$PS=betan$$θae−$$ae=btan$$θ$$a(1$$−$$e2)$$                                              $$=abtan$$θ                                  So  α$$=$$π$$2$$.

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

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