Reviewing: find eqn for parabola w/ vertex (3, 2), focus (1,

[Guest]

Find the equation for the parabola with vertex (3,2) and focus (1,2)

I know the standard equation for a parabola with the opening facing left is

(y-k)^2=4p(x-h) so how do I find the equation from here? if y^2=4px do I just substitute for x and y from the vertex and find p?

When I do I get p=1/3 but I think that is wrong. Can someone remind me how to do this problem? Thanks

 

[galactus]

p is the distance between the focus and the vertex.

The parabola opens left. p=2, because 3-1=2

\(\displaystyle \L\\(y-k)^{2}=4p(x-h)\)

h and k are the vertex coordinates.

\(\displaystyle \L\\(y-2)^{2}=8(x-3)\)

\(\displaystyle \L\\x=\frac{1}{8}y^{2}-\frac{1}{2}y+\frac{7}{2}\)