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Rotating a Hyperbola

  1. Jul 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Rotate the axis to eliminate the xy-term. Sketch the graph of the equation showing both sets of axis.


    2. Relevant equations

    3. The attempt at a solution


    First I find the angle of the x' y' axis.

    I find it to be[tex]\theta=\frac{\pi}{4}[/tex]

    Then find the x' and y' components

    by using the second 2 equations I listed I come out with.

    Then comes the substitutions and simplifying.




    I complete the square and end up with


    then I would divide though to get a 1 on the RHS but this is wrong.

    The answer should be.

    [tex] \frac{(x'-3\sqrt{2})^2}{16}-\frac{(y'-\sqrt{2})^2}{16}=1[/tex]

    where did I go wrong?
  2. jcsd
  3. Jul 17, 2010 #2
    Never mind. I found my problem.
  4. Jul 17, 2010 #3


    User Avatar
    Homework Helper

    It is correct up to here, but you mixed + and - after, and you made a mistake when multiplying the equation with 2.

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