Chapter 11.3, Problem 82STP

To determine

Find the center and radius of the circle and graph the circle.

Answer to Problem 82STP

Center ( − 3, − 7) and radius is 9

Explanation of Solution

Given:

The equation of circle is ${(x+3)}^2+{(y+7)}^2=81$

Concept Used:

The general equation of circle is ${(x-h)}^2+{(y-k)}^2=r^2$ , where $\text{center}(h,k)\text{and}\text{radius}=r$

Calculation:

Comparing both equations: ${(x-h)}^2+{(y-k)}^2=r^2$ and ${(x+3)}^2+{(y+7)}^2=81$

${(x-h)}^2+{(y-k)}^2=r^2$ center $(h,k)$ and radius $=r$   ${(x+3)}^2+{(y+7)}^2=81$   $h=-3;k=-7;r=\sqrt{81}=9$ Center ( − 3, − 7) and radius is 9

The graph of the circle ${(x+3)}^2+{(y+7)}^2=81$