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Homework Help: Finding the equation of a hyperbola given certain conditions

  1. Mar 17, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the equation of the hyperbola whose transverse axis is x = 3 and goes through:

    The vertices of 2x^2 + y^2 - 28x + 8y + 108 = 0 and the center of
    x^2 + y^2 - 6x + 4y + 3 = 0.

    2. Relevant equations
    (x - h)^2/a^2 - (y - k)^2/b^2 = 1

    3. The attempt at a solution
    so far I have identified the vertices of the ellipse and the center of the circumference, as you can see here:


    But now I don't have any idea how to proceed next. Could you help me please?
  2. jcsd
  3. Mar 17, 2013 #2


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    hi supermiedos! :smile:
    nooo, it's the centre of the circle :wink:

    (how can a circumference have a centre? :confused:)
  4. Mar 17, 2013 #3


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    A little nitpick, but this is the wrong equation. The equation you wrote requires a horizontal transverse axis.

    If the center of the circle is a point on the hyperbola, then surely this point is also one of the two vertices of the hyperbola, is it not? See if you can take it from there.
    Last edited: Mar 17, 2013
  5. Mar 18, 2013 #4
    :tongue: you are right, my bad
  6. Mar 18, 2013 #5
    Thank you for your help, I finally did it. Thank you so much
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