Equation of circle in quarter/half of a circle

1. The problem statement, all variables and given/known data

I am curious why is the equation of a quarter of a circle ($$y = \pm \sqrt{r^{2}-x^2}$$) 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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 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.

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 Quote by TsAmE 1. The problem statement, all variables and given/known data I am curious why is the equation of a quarter of a circle ($$y = \pm \sqrt{r^{2}-x^2}$$) the same as half a circle? Shouldnt they be different?
Actually, they are different if you include restrictions on x. For example, the equation for the upper right quarter circle is
$$y = +\sqrt{r^{2}-x^2}, 0 \le x \le r$$

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

For the upper half of the circle, you have $-r \le x \le r$

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