Explanation

(a)
Given parametric curves are
$x = 5t^{2} + \ 2,\ \ y = 10\ t + 4$
or $\frac{x - 2}{5} = t^{2},\ \frac{y - 4}{10} = t$
$\Rightarrow \ \frac{x - 2}{5} = \ \left( \frac{y - 4}{10} \right)^{2}$
$\Rightarrow \ (y - 4)^{2} = 20(x - 2)$
$\Rightarrow \ Y^{2} = 20X,\ where\ Y = y - 4,\ X = x - 2$
$\therefore$ Coodinates of focus are (5, 0)
$ie$, $x - 2 = 5,\ y - 4 = 0$
$\Rightarrow \ \ x = 7,\ y = 4$
Hence, required coordinates are (7, 4)