The locus of point from which the two tangents drawn to a parabola be such that slope of one is thrice of the other is

Let P be $(h,k)$. 

Any tangent to $y^2=4ax$ is  $y=mx+a/m$

 $k=mh+a/m\text{ ⇒ }{m}^{2}h-mk+a=0$

Its roots are $m_1\text{ and }3m_1\therefore m_1+3m_1=k/h$.

$m_1\cdot 3m_1=a/h$

Eliminate $m_1.\therefore \text{ Locus is }3y^2=16ax\text{. }$