Answer
(a) Focus: $F(\frac{1}{8},0)$
Directrix: $x=-\frac{1}{8}$
$Focal~diameter=\frac{1}{2}$
(b)
Work Step by Step
Equation of a parabola with horizontal axis: $y^2=4px$
$x=2y^2$
$y^2=\frac{1}{2}x$
$4p=\frac{1}{2}$
$p=\frac{1}{8}$
Focus: $F(p,0)=F(\frac{1}{8},0)$
Directrix: $x=-p=-\frac{1}{8}$
$Focal~diameter=|4p|=\frac{1}{2}$