The coordinates of the focus of the parabola described parametrically by $x=5t^2+2,y=10t+4$  are  
 

Given parametric curves are
$\begin{array}{l}x=5t^2+2,y=10t+4\\ or\frac{x-2}{5}=t^2,\frac{y-4}{10}=t\\ \Rightarrow \frac{x-2}{5}={\left(\frac{y-4}{10}\right)}^2\\ \Rightarrow {(y-4)}^2=20(x-2)\end{array}$

$\Rightarrow Y^2=20X,$
 where  $Y=y-4,X=x-2$
 Coordinate of focus is (5,00
ie,  $x-2=5,y-4=0$ 
$\Rightarrow x=7,y=4$
Hence , the required coordinate is (7,4)