Answer
(a) Focus: $F(-\frac{5}{4},0)$
Directrix: $x=\frac{5}{4}$
$Focal~diameter=5$
(b)
Work Step by Step
Equation of a parabola with horizontal axis: $y^2=4px$
$x+\frac{1}{5}y^2=0$
$\frac{1}{5}y^2=-x$
$y^2=-5x$
$4p=-5$
$p=-\frac{5}{4}$
Focus: $F(p,0)=F(-\frac{5}{4},0)$
Directrix: $x=-p=\frac{5}{4}$
$Focal~diameter=|4p|=5$
