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Q is a point on the auxiliary circle corresponding to the point P of the ellipse ` x^2 /a^2 + y^2/ b^2 =1`. If T is the foot of the perpendicular dropped from the focus S onto the tangent to the auxiliary circle at Q then the `Delta SPT` is |
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Answer» Tangent at point `Q(a cos theta, a sin theta)` `x cos theta+ y sin theta`=a ST=`|ae cos theta-a|=a(1-ecostheta)` S(ae,0) ST=`|(aecos theta-a)/sqrt(cos^2 theta+sin^2 theta)|=a(1-ecostheta)` SP=epm=e`(a/e-acostheta)` SP=`a-aecostheta` SP=a`(1-ecostheta)` so, SP=ST `/_SPT` is an isosceles triangle. |
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