The locus of the point of intersection of perpendicular tangents to the parabola $y^2=4x$ is.

Let $y=mx+\frac{a}{m}$ be  any tangent to $y^2=4ax$.

 Let $P\left(x_1,y_1\right)$ be the point of intersection 

$\Rightarrow y_1=m{x}_1+\frac{a}{m}\Rightarrow x_1{m}^2-x{y}_{1}m+a=0$ which is a quadratic equation in m.

If $m_1,m_2$ are the slopes of the two tangents then $m_1,m_2$ are the roots of the equation. 

Since, the tangents are perpendicular $m_1{m}_2=-1\Rightarrow \frac{a}{x_1}=-1\Rightarrow a=-x_1\Rightarrow x_1+a=0$

$\therefore \text{ Locus of }P\left(x_1,y_1\right)\text{ is }x+a=0$