If S be the focus of the parabola and the tangent and the normal at any point P meet the axes in T and G respectively, then 

Let $P\left(x_1,y_1\right)$ be any point on the parabola $y^2=4ax$

The equation of any tangent and any normal at $P\left(x_1,y_1\right)$

are

$y{y}_1=2a\left(x+x_1\right)$ and $\frac{y-y_1}{y_1}=-\frac{x-x_1}{2a}$

Since the tangent and the normal meet its axis at T and

G, respectively, so the co-ordinates of T and G are $(-x_1,0)$

and $\left(x_1+2a,0\right)$, respectively. 

Thus, $SP=PM=x_1+a$

$SG=AG-AS=x_1+2a-a=x_1+a$

and $ST=AS+AT=a+x_1$

Hence, $SP=SG=ST$.