Answer
Vertex: $(0,0)$
Focus: $\left(-\dfrac{D}{4C},0\right)$
Directrix: $x=\dfrac{D}{4C}$
Work Step by Step
We are given the equation:
$Cy^2+Dx=0$, $C\not=0,D\not=0$
Rewrite the equation:
$Cy^2=-Dx$
$y^2=-\dfrac{D}{C}x$
The equation is in the form:
$(y-k)^2=4p(x-h)$
Therefore the equation is that of a parabola. Because the equation contains $y^2$, the parabola is horizontal, and its axis is horizontal.
Determine $h,k,p$:
$h=0$
$k=0$
$4p=-\dfrac{D}{C}\Rightarrow p=-\dfrac{D}{4C}$
Determine the vertex:
$(h,k)=(0,0)$
Determine the focus:
$(h+p, k)=\left(0-\dfrac{D}{4C},0\right)=\left(-\dfrac{D}{4C},0\right)$
Determine the directrix:
$x=k-p$
$x=0-\left(-\dfrac{D}{4C}\right)$
$x=\dfrac{D}{4C}$
