Please help! What is the equation of the parabola, in vertex form, with focus at (2,-4) and directrix y = -6?

A. (x-2)^2=4(y+5)

B. (x-2)^2=-1/4(y+5)

C. (y+4)^2=-4(x-2)

D. (x+2)^2=1/4(y+4)

Question

Please help! What is the equation of the parabola, in vertex form, with focus at (2,-4) and directrix y = -6?

A. (x-2)^2=4(y+5)

B. (x-2)^2=-1/4(y+5)

C. (y+4)^2=-4(x-2)

D. (x+2)^2=1/4(y+4)

anonymous · Answer

@Hero when you get a chance do you think you could help me with this?

anonymous · Answer

I am assuming directrix y = -6 means the y intercept?

anonymous · Answer

I guess so, I don't really know much on this subject which is why I am asking for help :(

anonymous · Answer

Okay, no proplem. Ill figure it out :).

anonymous · Answer

Thank you so much, I really appreciate any help I can get! :)

hero · Answer

The vertex of the parabola is equidistant from the focus and the directrix. The directrix is not on the parabola, so the directrix cannot be the y-intercept.

hero · Answer

We know we have to use

y = a(x - h)^2 + k to solve this.

anonymous · Answer

Well if I know that the focus of the parabola is (2, -4) and that the directrix is y = -6, how would I write that into vertex form for a parabola equation?

anonymous · Answer

Oh okay, this is a dumb question, but what do the letters stand for? I have no idea where to plug what numbers into what letters!

hero · Answer

(h,k) is obviously the vertex of the parabola. 
a is like the vertical stretch/compression factor.

anonymous · Answer

think of Ax^2+Bx+C
and the vertex
(h,k)

anonymous · Answer

Would it be -6=a(x-2)^2 + -4 ?

hero · Answer

There's a key formula to know to solve this

$$c = \frac{1}{4|a|}$$

@ali1029, refrain from guessing. Please do not start guessing choices.

hero · Answer

Here's a better question...How did you come up with that as the answer?

hero · Answer

Explain yourself.

hero · Answer

You don't know what the vertex is yet.

hero · Answer

The focus is not the vertex.

anonymous · Answer

Okay, I apologize. I was just trying to make an effort. I got what I wrote down by plugging in the numbers where I thought they should go.

hero · Answer

Yeah, well...Nice try, but the focus is not the vertex.

hero · Answer

Let me see if I can sort of create something to help you out here

hero · Answer

So here's what we are given: https://www.desmos.com/calculator/znubqsjj06 Let me know if you can see it

hero · Answer

@mattpyne, I appreciate it if you would let me handle this

anonymous · Answer

Yes I can see the graph, what is it supposed to represent?

hero · Answer

It represents the given values of course. Take a closer look.

hero · Answer

The focus and directrix are given.

anonymous · Answer

Okay, I can see that now!

hero · Answer

Now...we know the vertex is equidistant from the focus and the directrix, so (2,-5) is the vertex.

hero · Answer

https://www.desmos.com/calculator/iy7yqpefic

hero · Answer

@mattpyne, I know you are trying to help, but I got this

anonymous · Answer

Thank you @mattpyne! Hero, now that we know what the vertex is what is the next step?

hero · Answer

Well, I need to suspend @mattpyne real quick hang on

hero · Answer

@mattpyne already gave you the answer

hero · Answer

I don't really see any point in continuing here

anonymous · Answer

Okay, well I didn't know whether the answer he gave me was correct or not, but that's fine. Thanks for the help.

hero · Answer

I understand @ali1029, but what @mattpyne did is what I consider very rude.

hero · Answer

He didn't read the code of conduct and has no idea how this site works.