Question

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

Answer 1

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?

Answer 2

Wouldn't the parabola open downwards?

Answer 3

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?

Answer 4

I lied, plug -9 in for p.

Answer 5

P is (x,y)

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

It sure is!