Answer
Vertex = $(0,0)$;
Focus $=\left(0, \dfrac{1}{32}\right)$;
Directrix $y=-\dfrac{1}{32}$;
Axis of symmetry $x=0$
Work Step by Step
We are given that $x^2=\dfrac{1}{8} y$
This equation has the form as $x^2 =4py$ wherein $4p=1/8 \implies p=1/32$
Here, the vertex is $(0,0)$ and the axis of symmetry is the $y$-axis, that is, $x=0$
and the $x$-term is squared, which shows that the parabola is vertical with focus $(0,p)=\left(0, \dfrac{1}{32}\right)$.
Now, the directrix is $y=-p=-\dfrac{1}{32}$
Our results are:
Vertex =$(0,0)$;
Focus $=\left(0, \dfrac{1}{32}\right)$;
Directrix $y=-\dfrac{1}{32}$;
Axis of symmetry $x=0$.
