## anonymous one year ago Find the standard form of the equation of the parabola with a focus at (0, -3) and a directrix at y = 3.

1. anonymous

@Astrophysics

2. anonymous

@phi

3. phi

it helps to plot the directrix and the focus

4. anonymous

Well I know the vertex is (0,0)

5. phi

|dw:1436389666695:dw|

6. anonymous
7. phi

yes the vertex is half way between them, so at (0,0) people label the vertex (h,k)

8. phi

and we know the parabola "surrounds" the focus so it looks (something) like |dw:1436389795339:dw|

9. phi

(y-k)= a(x-h)^2 with (h,k)= 0 and a will be negative y = ax^2 we need to find a

10. phi

I think people write it as $4 p y = x^2$ and p is the distance from the vertex to the focus (or vertex to the directrix) p=3 and negative because it's facing down -12y= x^2 so $y= -\frac{1}{12} x^2$

11. anonymous

Thanks. I understand. I have a few more questions but i'll post new forms. Thanks again, @phi