Write the equation of a parabola with a vertex at (5, 2) and a directrix y = 1??

Question

anonymous · Answer

first do you know what this would look like?

anonymous · Answer

because the directrix is a horizontal line and the vertex lies above the directrix, it will look something like this |dw:1374172264433:dw|

anonymous · Answer

that means the $x$ part is squared and so you will have something that looks like 
$$4p(y-k)=(x-h)^2$$ where the vertex is $(h,k)$ so in your case it is going to be 
$$4p(y-2)=(x-5)^2$$

anonymous · Answer

now all you need is $p$ which is the distance between the vertex and the directrix

anonymous · Answer

From my notes, this is how the equation is supposed to be set up

anonymous · Answer

the distance between $(5,2)$ and $y=1$ is 1, so $p=1$ and the equation should be 
$$4(y-2)=(x-5)^2$$

anonymous · Answer

no matter, divide both sides by 4 to get what you want

anonymous · Answer

ok, that makes more sense now, thank you!

anonymous · Answer

yw

anonymous · Answer

lets check the answer $y-2=\frac{1}{4}(x-5)^2$ and see if it is right http://www.wolframalpha.com/input/?i=parabola+%28y-2%29%3D1%2F4%28x-5%29^2 yup looks good