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Math Help - pre-calculus question with circle

  1. #1
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    pre-calculus question with circle

    The circle x2+y2-4x-6y+k=0 touches the x axis at the point t. Find the value of k and the coordinates of t.
    I got square root of 52-k for the radius but dont know what to do next.
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  2. #2
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    Dear milan,

    the equation of normal unit circle is:
    x^2 + y^2 = 1.

    The general circle can have other radius, can shift along x-axis and along y-axis, so the equation of general circle is:
    (x-a)^2 + (y-b)^2 = r^2.

    I suggest you that convert the original equation to such form and all will be happy.

    I think sqrt(52) is false result.
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  3. #3
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    Circle touching x-axis

    Hello milan
    Quote Originally Posted by milan View Post
    The circle x2+y2-4x-6y+k=0 touches the x axis at the point t. Find the value of k and the coordinates of t.
    I got square root of 52-k for the radius but dont know what to do next.

    The circle intersects the x-axis where y = 0. So put y = 0 in the equation and you get:

    x^2 - 4x \dots

    This is a quadratic equation in x. If the circle touches the x-axis, it must have equal roots. So? Can you see what to do next?

    Grandad
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