# How to determine b in a conic hyperboal graph

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In summary, to determine "b" in a conic hyperbola graph, you need a point off the x-axis or the equation of the asymptotes. Without these, it is difficult to solve for b accurately. However, by using a point off the x-axis or approximating the equation of the asymptote, you can get an approximate value for b.
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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?

## The Attempt at a Solution

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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.

I see, thanks!

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.

## 1. How do you find the center of a hyperbola?

The center of a hyperbola can be found by taking the average of the x and y coordinates of the two vertices.

## 2. What is the equation for a hyperbola?

The standard equation for a hyperbola is (x - h)^2/a^2 - (y - k)^2/b^2 = 1, where (h,k) is the center of the hyperbola and a and b are the distances from the center to the vertices along the x and y axes, respectively.

## 3. How do you determine the value of a in a hyperbola?

The value of a in a hyperbola can be found by taking the square root of the positive coefficient in the denominator of the x term in the standard equation. For example, in (x - 3)^2/25 - (y - 4)^2/16 = 1, a would be equal to 5.

## 4. How is the value of b related to the shape of a hyperbola?

The value of b in a hyperbola determines the steepness of the curve. A larger b value will result in a narrower, more elongated hyperbola, while a smaller b value will result in a wider, flatter hyperbola.

## 5. Can the value of b in a hyperbola be negative?

Yes, the value of b in a hyperbola can be negative. This indicates that the hyperbola is oriented in the opposite direction from a standard hyperbola, with the branches opening to the left and right instead of up and down.

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