The co-ordinate of the focus of the parabola described parametrically by $x=5t^2+2$  , $y=10t+4$ is 

Equation of parabola
 $$\begin{gathered} x=5t^2+2,y=10t+4 \\ {t}^2=\frac{x-2}{5},t=\frac{y-4}{10}\Rightarrow \frac{x-2}{5}={\left(\frac{y-4}{10}\right)}^2 \\ \Rightarrow {(y-4)}^2=20(x-2) \end{gathered}$$
$Y^2=20X$, where $Y=y-4,X=x-2$
 $x-2=5,y-4=0$
Focus (7,4)