How to determine b in a conic hyperboal graph

[Nope]

How to determine "b" in a conic hyperboal graph

Homework Statement

http://img143.imageshack.us/img143/3391/91667159.jpg
(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?

Homework Equations

The Attempt at a Solution

 

[Dick]

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.

 

[Nope]

I see, thanks!

 

[HallsofIvy]

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.