# Thread: Finding an equation for a hyperbola given the foci and asymptotes

1. ## Finding an equation for a hyperbola given the foci and asymptotes

Hi all,

I have the question:

Find an equation of the hyperbola having foci at (-1,1-√52) and (-1,1+√52) and the asymptotes at y=2/3x+5/3 and y=-2/3x+1/3

I know in this equation c^2 = 52 and c = +-√52

I also know the center is (-1,1). I also know by looking at the foci the graph is opening vertically I believe.

I have graphed the asymptotes as well.

I just dont understand how to find A and B. I know it has to do with the slope (2/3) and something with a/b = 2/3 but I have been looking at examples online and I don't understand. From what I've been taught after you find either A or B then you substitute the information into the equation C^2 = A^2 + B^2. Any help would be greatly appreciated thanks

2. ## Re: Finding an equation for a hyperbola given the foci and asymptotes

Originally Posted by subway69
Hi all,

I have the question:

Find an equation of the hyperbola having foci at (-1,1-√52) and (-1,1+√52) and the asymptotes at y=2/3x+5/3 and y=-2/3x+1/3

I know in this equation c^2 = 52 and c = +-√52

I also know the center is (-1,1). I also know by looking at the foci the graph is opening vertically I believe.

I have graphed the asymptotes as well.

I just dont understand how to find A and B. I know it has to do with the slope (2/3) and something with a/b = 2/3 but I have been looking at examples online and I don't understand. From what I've been taught after you find either A or B then you substitute the information into the equation C^2 = A^2 + B^2. Any help would be greatly appreciated thanks
You are supposed to know that the slope of the asymptote is determined by:

$\frac ab = \frac23~\implies~a = \frac23 b$

Since you know c^2 you are able to determine a and b.

3. ## Re: Finding an equation for a hyperbola given the foci and asymptotes

I think the the thing confusing you is upper case and lower case letters. Solve the equations

$\frac{a}{b}=\frac{2}{3}$ and $c^2=a^2+b^2$

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### The equation of hyperbola with foci and equation of asymptote

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