## Conics

1. The problem statement, all variables and given/known data

Graph the following. Include center, verticies, foci, asymptote, and directrix as appropriate.

2. Relevant equations

$$x^2 + 8y - 2x = 7$$

3. The attempt at a solution

So far I have:

V = (1, -7/8)
P = -2
X = -1

I have no clue where to go from here, or if I'm even right.
Thanks
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 Recognitions: Homework Help Science Advisor Don't you have to decide what kind of conic it is first? Complete the square in x and try to write it in some kind of normal form.
 when i completed the square i got $$(x-1)^2 = 8(-y+\frac{7}{8})$$

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## Conics

I think you mean (x-1)^2=8*(1-y). Try that once more. It's a parabola, isn't it?
 why would it be 8(y-1) ? What happened to the 7? How do you tell that it's a parabola? Because of the (x-1)^2?
 Recognitions: Homework Help Science Advisor Yes, because it's quadratic in x and linear in y. The 7 changed to an 8 when you added the 1 to both sides to complete the square. You did do that, right?
 oh nooes. I didn't. ok i got it. Now what?
 Recognitions: Homework Help Science Advisor Ok, now where is the vertex? And if you tell me what X and P are supposed to be I might be able to help you with those. Tomorrow. zzzzzzzzzzz.
 Ok thanks for all of your help! I got: v = (1, 1) p = 2
 So does that look right? If so, where do I go from here?
 really I think my problem is putting the initial equation in the $$\frac{(y-y0)^2}{a^2}-\frac{(x-x0)^2}{b^2}$$
 Mistake. I know it's a parabola because it's in the form $$(x-1)^2=8(1-y)$$. And I know p is 2 and the vertex is at (1,1). But how do I know which direction from V to go two units? Up or down? Left or right? Also how do I find the asymptote?
 Recognitions: Homework Help Science Advisor You never told me what P is. Is it the distance from the vertex to the focus? Does a parabola have any asymptotes?
 P = 2 right? Right now I have: $$v=(1,1)$$ $$p=2$$ $$F=(1,3)$$ $$Directrix=(1,-2)$$ Does that look right?
 Recognitions: Homework Help Science Advisor You've got the vertex. Now does the parabola go up or down from the vertex? As x gets large does y increase to +infinity or -infinity? And the directrix is a line, not a point.
 the parabola opens up.

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