# How to determine b in a conic hyperboal graph

1. Dec 10, 2009

### Nope

How to determine "b" in a conic hyperboal graph

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

http://img143.imageshack.us/img143/3391/91667159.jpg [Broken]
(x-1)2/22 - y2/b2 =1
I can't find any good point for me to solve b..I don't know what to do..
Is there any way to solve b without using the point?
2. Relevant equations

3. The attempt at a solution

Last edited by a moderator: May 4, 2017
2. Dec 10, 2009

### Dick

Re: How to determine "b" in a conic hyperboal graph

Not really. You need a point off the x-axis to solve for b. It looks like it passes near the point (4,1). That will let you get an approximate value for b.

3. Dec 11, 2009

### Nope

Re: How to determine "b" in a conic hyperboal graph

I see, thanks!

4. Dec 11, 2009

### HallsofIvy

Staff Emeritus
Re: How to determine "b" in a conic hyperboal graph

What you really need, in order to find b, is the equation of asymptotes. If a hyperbola has equation
$$\frac{(x-x_0)^2}{a^2} - \frac{(y-y_0)^}{b^}= 1$$
then its asymptotes are $y-y_0= \pm b(x-x_0)/a$

On this graph, it looks to me like an asymptote passes through (1,0) and (3,1) so has equation y= (1/2)(x- 1). That gives you a slightly different answer than assuming the graph passes through (4,1) but Dick and I are both "eyeballing" the graph.