Answer
Standard Form: $(x - \frac{1}{2}) ^2 + y^2 =\frac{1}{4}$
General Form: $x^2 +y^2 - x = 0$
Refer to the graph below.
Work Step by Step
The standard form of a circle's equation is $(x−h)^2+(y−k)^2=r^2$ where $r$=radius and $(h,k)$ is the center.
Substitute $r=\frac{1}{2}, h=\frac{1}{2}, \text{ and } k=0$ in the standard form above to obtain:
$$\left(x−\frac{1}{2}\right)^2+(y-0)^2=\left(\frac{1}{2}\right)^2\\
\left(x-\frac{1}{2}\right)^2+y^2=\frac{1}{4}$$
The general form of the equation of a circle is $x^2+y^2+ax+by+c=0$..
Subtract $\frac{1}{4}$ from each side of the equation above to obtain:
\begin{align*}
\left(x-\frac{1}{2}\right)^2+y^2−\frac{1}{4}&=0\\
x^2-x+\frac{1}{4}+y^2-\frac{1}{4}&=0\\
x^2+y^2-x&=0
\end{align*}
With $r=\frac{1}{2}$ and center at $\left(\frac{1}{2},0\right)$, plot the points $\frac{1}{2}$ units directly above, below, to the left, and to the right of the circle$. Then, connect these four points using a smooth curve to form a circle.
Refer to the graph above.
