Question

write the standard form of the equation of the circle with the given center and radius. center (6,1), r = \sqrt{5}
the equation of the circle in standard form is
(simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

The standard - form 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: Substitute given values

Given that $h = 6$, $k = 1$, and $r=\sqrt{5}$, we substitute these values into the formula: $(x - 6)^2+(y - 1)^2=(\sqrt{5})^2$.

Step3: Simplify the right - hand side

Since $(\sqrt{5})^2 = 5$, the equation of the circle in standard form is $(x - 6)^2+(y - 1)^2=5$.

Answer:

$(x - 6)^2+(y - 1)^2=5$