Question

write the standard form of the equation of the circle having the given radius and center. then, graph the circle.
r = 2, center: (\frac{1}{2},0)
equation:

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Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step2: Identify values of $h$, $k$, and $r$

Given that $h=\frac{1}{2}$, $k = 0$, and $r = 2$.

Step3: Substitute values into the formula

Substitute $h=\frac{1}{2}$, $k = 0$, and $r = 2$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-\frac{1}{2})^2+(y - 0)^2=2^2$, which simplifies to $(x-\frac{1}{2})^2+y^2 = 4$.

Answer:

$(x-\frac{1}{2})^2+y^2 = 4$