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Math Help - Finding circle coordinates given center, radius and x value only.

  1. #1
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    Finding circle coordinates given center, radius and x value only.

    Center is at 0,1044 why 1044? because of pixels.

    radius is also 1044.

    Please take a look at my picture now.

    I want to find the coordinates of the points on the circle, given the x value: 1 2 3 4 5......... so on.
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  2. #2
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    Quote Originally Posted by stillblazin View Post
    Center is at 0,1044 why 1044? because of pixels.

    radius is also 1044.

    Please take a look at my picture now.

    I want to find the coordinates of the points on the circle, given the x value: 1 2 3 4 5......... so on.
    1. A circle with the center C(h, k) and the radius r is determined by the equation:

    (x-h)^2+(y-k)^2=r^2

    2. With the given data your circle has the equation:

    (x-0)^2+(y-1044)^2 = 1044^2

    3. To get the y-coordinates of a point you only have to plug in the x-value and solve the equation for y:

    x^2+(y-1044)^2 = 1044^2~\implies~|y-1044| = \sqrt{1044^2-x^2} which "simplifies" to:

    y=1044+\sqrt{1044^2-x^2}~\vee~y=1044-\sqrt{1044^2-x^2}

    Example: x = 10:

    y = 1044+\sqrt{1044^2-100}~\approx~2087.95~\vee~y = 1044-\sqrt{1044^2-100}~\approx~0.048
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