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Math Help - anyone who can help me with this problem:

  1. #1
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    anyone who can help me with this problem:

    find the length of the chord 3x-y+9=0
    of the circle x^2+y^2=5
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  2. #2
    Member
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    Mumbai
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    One can see a very dull method here.

    Solve the two equations for the points of intersection,

    y=3x+9

    x^2+y^2=5

    Therefore,

    x^2 + 9(x+3)^2=5

    10x^2 + 54x+81=5

    5x^2+27x+38=0

    so discriminant of this equation=729-760< 0

    i.e. the line doesn't meet the given circle at all

    I think you've made a typing mistake in your question.
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  3. #3
    MHF Contributor red_dog's Avatar
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    Medgidia, Romania
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    You have to solve the system

    \left\{\begin{array}{ll}x^2+y^2=5\\3x-y+9=0\end{array}\right.

    From the second ecuation y=3x+9. Replace y in the first equation. We get the quadratic

    5x^2+27x+38=0

    But the discriminant is \Delta =-31<0, so the system has no real solution. That means the line doesn't intersect the circle.
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