Chapter 13, Problem 4CR

To determine

To calculate the center and radius of circle.

Answer to Problem 4CR

The center and radius of circle is,

  $r=7\text{ and }c=(5,-1)$

Explanation of Solution

Given information: equation of the circle is ${(x-5)}^2+{(y+1)}^2=49$

Formula used:

Equation of circle ${(x-h)}^2+{(y-k)}^2=r^2$ with $(h,k)$ as center and $r$ as radius.

Calculation:

The given equation is ${(x-5)}^2+{(y+1)}^2=49$

Now rewriting the equation as ${(x-5)}^2+{(y-(-1))}^2=7^2$

Now comparing it with equation of circle ${(x-h)}^2+{(y-k)}^2=r^2$ we have radius, $r=7$ and center, $c=(5,-1)$