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Equation of circle in quarter/half of a circle

  1. Aug 28, 2010 #1
    1. The problem statement, all variables and given/known data

    I am curious why is the equation of a quarter of a circle ([tex]y = \pm \sqrt{r^{2}-x^2}[/tex]) the same as half a circle? Shouldnt they be different?

    2. Relevant equations


    3. The attempt at a solution

  2. jcsd
  3. Aug 28, 2010 #2
    If you want quarter circle you have to use either + (for positive quarter) and - (for negative quarter) in the equation you mentioned.
    For getting half circle both + and - ve values of equation are considered.
  4. Aug 28, 2010 #3


    Staff: Mentor

    Actually, they are different if you include restrictions on x. For example, the equation for the upper right quarter circle is
    [tex]y = +\sqrt{r^{2}-x^2}, 0 \le x \le r[/tex]

    The equation for the upper left quarter circle has a different restriction on x; namely
    [tex] -r \le x \le 0[/tex]

    For the upper half of the circle, you have [itex]-r \le x \le r[/itex]

    For the lower half circle and quarter circles, the only difference is that the negative square root is used.
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