question_answer

TP and TQ are tangents to the parabola \[{{y}^{2}}=4ax\] at P and Q. If the chord PQ passes through the fixed point [-a, b] then the locus of T is

A)  \[ay=2b(x-b)\]              

B)  \[bx=2a(y-a)\]

C)  \[by=2a(x-a)\]              

D)  \[ab=2b(y-b)\]

Correct Answer: C

Solution :

Chord of contact of (h, k) is \[ky\,=2a(x+h)\] . it passes through (-a, b) \[\Rightarrow \,\,bk=2a(-a+h)\] \[\Rightarrow \,\,\] Locus is by \[=2a(x-a)\].