Find the standard form of the equation of the parabola with a focus at $(0,−9)$ and a directrix $y=9.$

Question

welshfella · Answer

this parabola opens upwards and standard form is

x^2 = 4ay
where a is the y coordinate of the focus and y = -a is the directrix

so  can you work this one out?

anonymous · Answer

Wouldn't the parabola open downwards?

anonymous · Answer

It would. The form for a parabola is $$y = 1/4p(x-h)^2+k$$ From here you can plug 9 into p since p = distance between vertex and focus. The h and k values are both 0 since the vertex is at (0,0). Can you get it from here?

anonymous · Answer

I lied, plug -9 in for p.

anonymous · Answer

|dw:1439345400610:dw|

anonymous · Answer

P is (x,y)

anonymous · Answer

Hang on, I'm trying to solve it. :)

anonymous · Answer

Okay, post your answer here so I can check it for you :)

anonymous · Answer

So is it $y=-\frac{ 1 }{ 36 }x^2?$

anonymous · Answer

It sure is!