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Math Help - Is this problem a general for of the equation of a circle?

  1. #1
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    Is this problem a general for of the equation of a circle?

    -x^2-4x+4y^2+8y-22=0
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  2. #2
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    Hello, scottydoint!

    -x^2-4x+4y^2+8y-22\:=\:0

    It is not a circle . . . x^2 and y^2 have different coefficient.

    Since the coefficients of x^2 and y^2 have opposite signs, it is a hyperbola.

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  3. #3
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    Quote Originally Posted by scottydoint View Post
    -x^2-4x+4y^2+8y-22=0
    1. Complete the squares:

    -(x^2+4x{\bold{\color{red}+4}})+4(y^2+2y{\bold{\col  or{blue}+1}})=22 {\bold{\color{red}-4}} {\bold{\color{blue}+4}}

    2. Re-write:

    -x^2-4x+4y^2+8y-22=0~\implies~ -\dfrac{(x+2)^2}{22} + \dfrac{(y+1)^2}{5.5} =1

    3. This is the equation of a hyperbola opening up-down.
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