Find the equation of the parabola with vertex (0,0) and focus (0,1)?

Answer 1

The vertex and focus are in a vertical line with the focus above the vertex. So the parabola is vertical and opens upwards. The equation of such a parabola with vertex (h,k) is:

4p(y - k) = (x - h)²

The vertex (h,k) = (0, 0).

The directed distance from the vertex to the focus is p.

p = 1 - 0 = 1
4p = 4

The equation of the parabola is:

4p(y - k) = (x - h)²
4(y - 0) = (x - 0)²

4y = x²

or

y = (1/4)x²

Answer 2

http://en.wikipedia.org/wiki/Parabola