Explanation

(a)
Given equation can be rewritten as
$(x + 3)^{2} = - 2\left( y - \frac{9}{2} \right)\$
$\Rightarrow \ \ \ \ X^{2} = 4AY$
where$\ X = x + 3,\ A = - \frac{1}{2},\ Y = y - \frac{9}{2}$
$\therefore$ Focus is $\left( 0,\ \frac{- 1}{2} \right)$
But$\ X = x + 3 = 0\$and$\ Y = y - \frac{9}{2} = - \frac{1}{2}$
$x = - 3,\ y = 4$
$\therefore$ Required focus is$\ ( - 3,\ 4\ )$