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

1. welshfella

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?

2. anonymous

Wouldn't the parabola open downwards?

3. anonymous

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?

4. anonymous

I lied, plug -9 in for p.

5. anonymous

|dw:1439345400610:dw|

6. anonymous

P is (x,y)

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. anonymous

It sure is!

11. anonymous

Wow thanks! I was working with this, but I got the vertex wrong. :( How would you find the vertex?

12. anonymous

No problem! Okay so the vertex is equidistant from both the focus and the directrix. Since they both are -9 away from the origin (as the x value for both is 0) you can tell that the vertex must be at the origin in order for it to be equidistant from both!

13. anonymous

Awesome! Thanks again. You're great! :)

14. welshfella

yes surit is correct - i misread the problem

15. welshfella

- and migillope also