Equation of circle in quarter/half of a circle

TsAmE

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

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3. The attempt at a solution

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n.karthick

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.

Mark44

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.