1.

If the tangents at the extremities of a chord PQ of a parabola intersectat T, then the distances of the focus of the parabola from the point P,T,Q are in :

Answer»

<P>AP
GP
HP
None of these

Solution :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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