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Math Help - Finding an equation for a hyperbola given the foci and asymptotes

  1. #1
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    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
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  2. #2
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    Re: Finding an equation for a hyperbola given the foci and asymptotes

    Quote Originally Posted by subway69 View Post
    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.
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  3. #3
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    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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