InterviewSolution
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InterviewSolution
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AB and CD are two equal and parallel chords of the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1. Tangents to the ellipse at A and B intersect at P and tangents at C and D at Q. The line PQ |
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Answer» passes through the origin `rArr` Equations of Ab and CD are `(X)/(a) alpha + (y)/(b) beta =1` and `(x)/(a) alpha_(1) +(y)/(b) beta_(1) =1` (Chord of CONTACT) These lines are parallel `rArr (alpha)/(alpha_(1)) = (beta)/(beta_(1)) =k` ALSO `(alpha^(2))/(alpha^(2)) +(beta^(2))/(b^(2)) = (alpha_(1)^(2))/(a^(2)) + (beta_(1)^(2))/(b^(2))` `rArr (alpha)/(alpha_(1)) = (beta)/(beta_(1)) =-1` `rArr PQ` passes through origin and is bisected at the origin. |
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