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 PQA. passes through the originB. is bisected at the originC. cannot pass through the originD. is not bisected at the origin

AB and CD are two equal and parallel chords of the ellipse `(x^(2))/(a

1.	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 PQA. passes through the originB. is bisected at the originC. cannot pass through the originD. is not bisected at the origin
Answer» Correct Answer - A::B Let P and Q be the points `(alpha, beta)` and `(alpha_(1),beta_(1))` `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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