Chapter 9.2, Problem 4OE

To determine

To calculate: The center and radius of the circle.

Answer to Problem 4OE

The center and radius of the circle are $\left(5,0\right)$ and $5$ respectively.

Explanation of Solution

Given information: The equation of the circle is ${\left(x-5\right)}^2+y^2=5$ .

Formula used: ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

Calculation: Comparing ${\left(x-5\right)}^2+y^2=5$ to ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , we get,

  $\begin{array}{ccc}\begin{array}{l}-h=-5\\ \therefore h=5\end{array}& \begin{array}{l}-k=0\\ \therefore k=0\end{array}& \begin{array}{l}{r}^2=25\\ \therefore r=5\end{array}\end{array}$

Here, the radius of the circle is 5.

Now, as we know that $\left(h,k\right)$ is the center of a circle.

Therefore, the center of the given circle $\left(h,k\right)=\left(5,0\right)$

Hence, the required center and radius of the circle are $\left(5,0\right)$ and $5$ respectively.