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Math Help - Determine the equation of a circle

  1. #1
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    Determine the equation of a circle

    Determine the standard equation for the circle
    C that passes through
    the points
    A
    (2, 0) and B(0, 4), and has centre lying on the line L : x+2y+4 = 0.

    Hint: First find the centre of C ; it has the same distance from A and B.

    Thanks for at least looking at the question
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  2. #2
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    Quote Originally Posted by mamt6 View Post
    Determine the standard equation for the circle
    C that passes through
    the points
    A
    (2, 0) and B(0, 4), and has centre lying on the line L : x+2y+4 = 0.

    Hint: First find the centre of C ; it has the same distance from A and B.

    Thanks for at least looking at the question
    let point C be (x,y) ...

    AC = BC

    (x-2)^2 + (y-0)^2 = (x-0)^2 + (y-4)^2

    x^2 - 4x + 4 + y^2 = x^2 + y^2 - 8y + 16

    -4x + 4 = -8y + 16

    -x + 1 = -2y + 4

    x = 2y-3

    since (x,y) lies on the line x+2y+4=0 ... x = -2y-4

    so ...

    -2y-4 = 2y-3

    solve for the y-coordinate of point C , then find its x-coordinate.

    then determine the equation of the circle ...

    (x - x_c)^2 + (y - y_c)^2 = r^2
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