Question

find the standard equation of the circle having the given center and radius. center (10,2), radius $\frac{5}{3}$. the equation of the circle is (type an equation. type your answer in standard form. use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Recall circle - standard - form 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 the values of $h$, $k$, and $r$

Given that the center is $(10,2)$, so $h = 10$, $k = 2$, and the radius $r=\frac{5}{3}$.

Step3: Substitute the values into the formula

Substitute $h = 10$, $k = 2$, and $r=\frac{5}{3}$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 10)^2+(y - 2)^2=(\frac{5}{3})^2$.

Step4: Simplify the right - hand side

$(\frac{5}{3})^2=\frac{25}{9}$, so the equation of the circle is $(x - 10)^2+(y - 2)^2=\frac{25}{9}$.

Answer:

$(x - 10)^2+(y - 2)^2=\frac{25}{9}$