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If the tangents at the extremities of a chord PQ of a parabola intersect at T, then the distances of the focus of the parabola from the point P,T,Q are in :A. APB. GPC. HPD. None of these |
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Answer» Correct Answer - B Let the equation of the parabola be `y^(2)=4ax` and `P("at"_(1)^(2),2"at"_(1)),Q("at"_(2)^(2),2"at"_(2))` be the extremitics of chod PQ, the coordinates of T, the point of intersection of tangents at P and Q. `("at"_(1)t_(2),a(t_(1)+t_(2)))` then `SP=a(1+t_(1)^(2)),SQ=a(1+t_(2)^(2))` and `ST^(2)=("at"_(1)t_(2)-a)^(2)+(a(t_(1)+t_(2))-0)^(2)` `=a^(2)(t_(1)^(2)+t_(2)^(2)+t_(1)^(2)+t_(2)^(2)+1)=a^(2)(1+t_(1)^(2))(1+t_(2)^(2))=SP.SQ`. |
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