Answer
(a) Focus: $F(0,-\frac{3}{8})$
Directrix: $y=\frac{3}{8}$
$Focal~diameter=\frac{3}{2}$
(b)
Work Step by Step
Equation of a parabola with vertical axis: $x^2=4py$
$8x^2+12y=0$
$8x^2=-12y$
$x^2=-\frac{3}{2}y$
$4p=-\frac{3}{2}$
$p=-\frac{3}{8}$
Focus: $F(0,p)=F(0,-\frac{3}{8})$
Directrix: $y=-p=\frac{3}{8}$
$Focal~diameter=|4p|=\frac{3}{2}$
