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

Question

anonymous · Answer

I think the answer is 
f(x)=1/4x^2 but i am not sure.

anonymous · Answer

no one likes these conic sections question do they?

mertsj · Answer

If the focus is (0,1) and the directrix is y=-1, then the vertex is (0,0) and the parabola is concave upward. So it's equation is: y = ax^2

anonymous · Answer

btw your answer is right, since the vertex is at $(0,0)$ which in one unit away from the directrix, you have $4py=x^2$ where $p=1$ so you can write it as 
$$y=\frac{1}{4}x^2$$

anonymous · Answer

Thank you! 
So in that case, if the focus is (-2,4) and the directrix is y= 6 then the vertex =(-2,5) and the parabola is concave downward, so its equation would be 
$$f(x)=1/4(x+2)^2+5$$

anonymous · Answer

Right?

anonymous · Answer

I'm sorry, the equation would be:
$$f(x)=-1/4(x+2)^2+5$$

mertsj · Answer

yes