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Math Help - Vertical Shift of Hyperbola

  1. #1
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    Vertical Shift of Hyperbola

    Question: Find formula for hyperbola with given information.

    foci (2,0), (2,8)
    asymptotes: y = 3 + x/2 and y = 5 - x/2

    My current equation is:
    \frac{(y-4)^2}{2^2} - \frac{(x-2)^2}{1^2} = 1

    My graph:


    I'm trying to figure out the last vertical shift.
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  2. #2
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    Quote Originally Posted by Sw0rDz View Post
    Question: Find formula for hyperbola with given information.

    foci (2,0), (2,8)
    asymptotes: y = 3 + x/2 and y = 5 - x/2

    My current equation is:
    \frac{(y-4)^2}{2^2} - \frac{(x-2)^2}{1^2} = 1

    ...
    According to the given information you know:

    Midpoint M(2, 4)

    \dfrac ab =\dfrac12~\implies~a=2b

    Distance of one focus to M is 4; therefore:

    a^2+b^2=16~\implies~4b^2+b^2=16

    Calculate the lengthes of a and b and determine the equation of the hyperbola.

    I've got:

    \dfrac{5(y-4)^2}{4^2}-\dfrac{5(x-2)^2}{8^2}=1
    Attached Thumbnails Attached Thumbnails Vertical Shift of Hyperbola-hyp_ausfoci.png  
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