# Formula for semi circle with diameter up?

So I know the formula for a semi circle is

$$y = \sqrt{r^2 - x^2}$$

However, what if I wanted to find the equation for a semi circle who's diameter is at the top of the graph?

Would this be the best solution?

$$y = r-\sqrt{r^2 - x^2}$$

Thanks

• Not sure what you are asking for. The result of what you are asking for is here: wolframalpha.com/input/… – gt6989b Feb 25 '14 at 21:44

The $r$ at the start is optional. It just shifts the semicircle up so the bottom is tangent to the $x$ axis. If you delete it the semicircle is below the $x$ axis. In both cases it has the orientation you desire. Good work.
It also can be $y=-\sqrt{r^2-x^2}$
• One way to see this is that the equation for the full circle, $\ x^2 + y^2 = r^2 \$ does not describe a single function (as it fails the "vertical line test"), but rather represents two separate functions, since $\ y = \pm \sqrt{r^2 - x^2} \ ,$ with the positive square-root corresponding to the curve for the "upper semi-circle" and the negative square-root, the "lower semi-circle". – colormegone Feb 25 '14 at 23:45