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Math Help - how do i graph a hyperbola from the following equation?

  1. #1
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    Unhappy how do i graph a hyperbola from the following equation?

    x^2-3y^2+8x-6y+4=0

    how do i find the center,transverse axis, vertices, foci and asymptotes from that equation??
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    Re: how do i graph a hyperbola from the following equation?

    Move all the x terms together, the y terms together, and put the equation into the standard form by completing the square on the x terms and the y terms.
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    Re: how do i graph a hyperbola from the following equation?

    Quote Originally Posted by alyse2526 View Post
    x^2-3y^2+8x-6y+4=0

    how do i find the center,transverse axis, vertices, foci and asymptotes from that equation??
    start by completing the square in x and y ...

    x^2 + 8x + 16 - 3(y^2 + 2y + 1) = -4 + 16 - 3

    (x + 4)^2 - 3(y + 1)^2 = 9

    \frac{(x+4)^2}{9} - \frac{(y+1)^2}{3} = 1

    now you have the hyperbola in the form ...

    \frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1

    go to this page and see how everything is related ...

    Hyperbola Formulas
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