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Analytics of an Arc

  1. Jan 30, 2004 #1
    The first general circle formula is,
    Where M(a,b) and r:radius.
    I understand this well, but when the subject is arcs...
    x_\textrm{1,2} =a (+-) \sqrt{r^2-(y-b)^2}
    My teacher said that equations for x1 and x2 were half circles at right and left. But how?
    And also the same fo y,
    were the arcs of top half and bottom of the circle. But why?
    Any help is appreciated.
  2. jcsd
  3. Jan 30, 2004 #2


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    Science Advisor

    You apparently accept that [tex](x-a)^2+(y-b)^2=r^2[/tex]
    is the equation of a circle.

    To get [tex]x_\textrm{1,2} =a (+-) \sqrt{r^2-(y-b)^2}[/tex], you solve for x. Of course, with the square root, you have to take + and - to get both roots.

    You know, I hope, that x measures right and left on a graph. The point (4,3) is 4 units to the right of the x-axis. The point (-4,3) is 4 units to the left. When you solve any equation for x, the result is "left" or "right". Taking the positive sign is right, negative, left.

    y measures up and down so solving for y does the same thing except up and down instead of right and left.
  4. Jan 31, 2004 #3
    I knew that basics but couldn't put together. Thanks anyway.
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