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Math Help - solving a conic intersection

  1. #1
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    solving a conic intersection

    find the intersection of these

    2x^2+2y^2-4x+9y+4=0
    x^2+y^2+x+12y+8=0

    its very hard.. it tried substitution and yielded complex numbers.. pls help
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  2. #2
    MHF Contributor

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    Have you tried: multiply the second equation by 2 and subtract from the first equation. That leaves a linear equation in x and y. Solve that for, say, y as a linear function of x and substitute into either of the original equations. That gives you a quadratic equation for x.

    Yes, such an equation might well have complex roots. If so, what would that tell you about the intersection of the two circles?
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