If the tangent at the extrenities of a chord PQ of a parabola intersect at T, then the distances of the focus of the parabola from the points P.T. Q are in

Options

A. AP
B. GP
C. HP
D. None of these

Answer

B

Explanation

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`.