Question

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

Answer 1

`8x^2+y=0`

Explanation:

Vertex is V(0, 0) and focus is `S(0, -1/32)`.

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 = `1/32`.

So, the equation of the parabola is `x^2=-4ay=-1/8y`.
Rearranging, `8x^2+y=0`.. .