# Thread: How to find focus of parabola

1. ## How to find focus of parabola

I have the equation: (y - 2)^2 = -8(x - 3)

I learned that the focus is the "-8" part which is the distance from the vertex, and the vertex from the equation is (3,2) and this parabola is opening up sideways to the left. So from (3,2), the focus would be 8 units into the left direction which would be at (-5,2) but apparently this is wrong.

How else would I find the focus?

2. ## Re: How to find focus of parabola

Oh, never mind I forgot to factor out the '4' in the equation

3. ## Re: How to find focus of parabola

Originally Posted by daigo
I have the equation: (y - 2)^2 = -8(x - 3)

I learned that the focus is the "-8" part which is the distance from the vertex
Then you learned wrong! The focal length is "given by" that number but is not equal to it. If a parabola is given by $\displaystyle (y- k)^2= 4p(x- h)$ then the focal length (distance from vertex to focus) is p. In your case, 4p= -8 so p= -2, not -8.

, and the vertex from the equation is (3,2) and this parabola is opening up sideways to the left. So from (3,2), the focus would be 8 units into the left direction which would be at (-5,2) but apparently this is wrong.

How else would I find the focus?