Part 2/5:
Rearranging the Equation
To better understand this, we can rearrange the equation to isolate ( y ):
Start with ( (y - b)^2 = r^2 - (x - a)^2 ).
Taking the square root yields ( y - b = \pm \sqrt{r^2 - (x - a)^2} ).
Therefore, we can express ( y ) in terms of ( x ) as ( y = b \pm \sqrt{r^2 - (x - a)^2} ).
This formulation indicates that the equation represents two functions—one corresponding to the upper semicircle and the other to the lower semicircle.