Question

Derive the equation from the parabola with a focus at (0,1) and a directrix of y=-1

Answer 1

Answer:

y = (x^2)/4

Step-by-step explanation:  

The vertex of this parabola is halfway between the focus (0,1) and the directrix y = -1.  Thus, the vertex is at (0,0).  The variable p represents the distance between focus and vertex, which is 1.  

Thus, adapting the general formula for the equation of a parabola, we have:

4(1)y=x^2, or 4y = x^2, or y = (x^2)/4.