# What is the equation of the parabola with a vertex at the origin and a focus at (0, -1/32)?

Apr 8, 2016

$8 {x}^{2} + y = 0$

#### Explanation:

Vertex is V(0, 0) and focus is $S \left(0 , - \frac{1}{32}\right)$.

Vector VS is in the y-axis in the negative direction. So, the axis of the parabola is from the origin and y-axis, in the negative direction, The length of VS = the size-parameter a = $\frac{1}{32}$.

So, the equation of the parabola is ${x}^{2} = - 4 a y = - \frac{1}{8} y$.
Rearranging, $8 {x}^{2} + y = 0$.. .