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Math Help - Help solving conics that are equal to zero, degenerate

  1. #1
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    Help solving conics that are equal to zero, degenerate

    If I have a conic in standard form (converted from 9x2 -4y2-36x-24y=0) of 9(x-2)2-4(y+3)2=0, how would I go about either solving or graphing this. If it were a plus sign between them I'd just give an answer of a point, but I have a strange feeling that there is more to the answer, a solution with an explanation would be greatly appreciated.
    Last edited by mikewezyk; November 25th 2012 at 09:48 AM.
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  2. #2
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    Re: Help solving conics that are equal to zero, degenerate

    this is a degenerate conic ...

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    Re: Help solving conics that are equal to zero, degenerate

    Hello, mikewezyk!

    \text{If I have a conic in standard form }\,9(x-2)^2 - 4(y+3)^2 \:=\:0
    . . \text{ converted from }\,9x^2 - 4y^2 - 36x - 24y \:=\:0
    \text{how would I go about either solving or graphing this?}

    If it were a plus sign between them, I'd just give an answer of a point, . Right!
    . . but I have a strange feeling that there is more to the answer. . Right again!
    A solution with an explanation would be greatly appreciated.

    We have: . 9(x-2)^2 - 4(y+3)^2 \:=\:0 \quad\Rightarrow\quad 4(y+3)^2 \:=\:9(x-2)^2

    . . . . . . . . (y+3)^2 \:=\:\tfrac{9}{4}(x-2)^2 \quad\Rightarrow\quad y + 3 \:=\:\pm\tfrac{3}{2}(x-2)

    . . . . . . . . y \;=\;-3 \pm\tfrac{3}{2}(x-2)


    These are the equations of the asymptotes of the hyperbola.
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