Question

`T P` and `T Q` are tangents to the parabola `y^2=4a x` at `Pa n dQ ,` respectively. If the chord `P Q` passes through the fixed point `(-a ,b),` then find the locus of `Tdot`

Answer 1

Correct Answer - by = 2a (x-a)
Let the point T be (h,k).
Equation of chord of contact to parabola `y^(2)=4ax` w.r.t. T is
ky=2a(x+h)
It passes through the point (-a,b).
`:." "bk=2a(-a+h)`
So, locus of point T is by=2a (x-a).