Explanation

(b)
Given equation is
$y^{2} - 8y - x + 19 = 0$
$\Rightarrow \ {(y - 4)}^{2} = x - 3$
$\Rightarrow \ Y^{2} = 4AX$, where $Y - y - 4,\ A = \frac{1}{4}$ and $X = x - 3$
$\therefore$ Focus is $(A,0) = \left( \frac{1}{4},\ 0 \right) = \left( \frac{13}{4},\ 4 \right)$
Vertex is $(0,\ 0) = (3,\ 4)$
Directrix is $x = - A\ \Rightarrow \ x - 3 = - \frac{1}{4}$
$\Rightarrow \ x = \frac{11}{4}$