# Equation of a Parabola Given Vertex and Focus

• May 13th 2009, 11:37 AM
Joanie
Equation of a Parabola Given Vertex and Focus
Hi--

I have to write an equation of a parabola with vertex (0,-6) and focus (0,5). p = 11

I have done it two ways and have gotten two different answers. I just need to know which one is correct.

1. y=p(x-h)^2+k
y=11(x-0)^2-6
y=11x^2-6

2. (x-h)^2=4p(y-k)
(x-0)^2 = 4(11)(y+6)
x^2 = 44(y+6)
x^2=44y + 264
x^2-264= 44y
(x^2-264)/44=44y/44
1/44x^2-6=y

Could you let me know which one of these is the correct equation? Thanks.
• May 13th 2009, 11:46 AM
masters
Quote:

Originally Posted by Joanie
Hi--

I have to write an equation of a parabola with vertex (0,-6) and focus (0,5). p = 11

I have done it two ways and have gotten two different answers. I just need to know which one is correct.

1. y=p(x-h)^2+k
y=11(x-0)^2-6
y=11x^2-6

2. (x-h)^2=4p(y-k)
(x-0)^2 = 4(11)(y+6)
x^2 = 44(y+6)
x^2=44y + 264
x^2-264= 44y
(x^2-264)/44=44y/44
1/44x^2-6=y

Could you let me know which one of these is the correct equation? Thanks.

Hi Joanie,

I'm going to go with door number 2.
• May 14th 2009, 08:24 AM
stapel
Quote:

Originally Posted by Joanie
1. y=p(x-h)^2+k

Shouldn't the "p" actually be an "a"...? (Blush)