Conics

duki

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

[tex]x^2 + 8y - 2x = 7[/tex]

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

Dick

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.

duki

when i completed the square i got [tex](x-1)^2 = 8(-y+\frac{7}{8})[/tex]

Dick

I think you mean (x-1)^2=8*(1-y). Try that once more. It's a parabola, isn't it?

duki

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?

Dick

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?

duki

oh nooes. I didn't.

ok i got it. Now what?

Dick

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.

duki

Ok thanks for all of your help!

I got:

v = (1, 1)
p = 2

duki

So does that look right? If so, where do I go from here?

duki

really I think my problem is putting the initial equation in the [tex]\frac{(y-y0)^2}{a^2}-\frac{(x-x0)^2}{b^2}[/tex]

duki

Mistake. I know it's a parabola because it's in the form [tex](x-1)^2=8(1-y)[/tex]. 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?

Dick

You never told me what P is. Is it the distance from the vertex to the focus? Does a parabola have any asymptotes?

duki

P = 2 right?
Right now I have:

[tex]v=(1,1)[/tex]
[tex]p=2[/tex]
[tex]F=(1,3)[/tex]
[tex]Directrix=(1,-2)[/tex]

Does that look right?

Dick

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.

duki

the parabola opens up.

Dick

I disagree. Why do you think so?