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DETERMINE the equation of the circle that has the following three points on its circumference: A(1,5), B(3,7) and C(5,5).

  • Math -

    (x-k)^2+ (y-h)^2 = r^2
    so
    (1-k)^2 + (5-h)^2 = r^2
    (3-k)^2 + (7-h)^2 = r^2
    (5-k)^2 + (5-h)^2 = r^2
    Now before I go off and solve those for k,h and r, sketch a graph
    Notice that two points, A and C are at the same height,5
    The third point,B, is half way between them (3 is halfway between 1 and 5)
    I conclude that the center of the circle is on x = 3
    so
    k = 3
    Onward
    (1-3)^2 + (5-h)^2 = r^2
    (3-3)^2 + (7-h)^2 = r^2
    (5-3)^2 + (5-h)^2 = r^2
    that second equation is pretty easy now.
    (7-h)^2 = r^2
    the first and third are actually the same now that we know what k isso use the first and the second
    4 + (5-h)^2 = r^2
    (7-h)^2 = r^2

    29 - 10 h + h^2 = r^2
    49 -14 h + h^2 = r^2
    ----------------------
    -20 +4 h = 0
    h = 5
    well I guess you can take it from there

  • Math -

    Thank you!

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