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Circle equation vs. semicircle equation

  1. Jan 20, 2013 #1
    This may sound like a dumb question, but...

    For the equation of a circle with a radius of 1, the equation is:

    x^2 + y^2 = 1


    But if we rearrange that to be: y= √(1 - x^2),
    then it's only a semicircle...

    Why is that? Why is it now a semicircle just because it got rearranged?

    Thanks!
     
  2. jcsd
  3. Jan 20, 2013 #2

    Mark44

    Staff: Mentor

    Your two equations are not equivalent, meaning that the first equation has more solutions than the second one.

    If you solve for y in the first equation, you should get y = ±√(1 - x2). The pos. square root represents the upper half circle; the neg. square root represents the lower half circle.
     
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