Chapter 8.3, Problem 11E

Solution

Graph the given equation of circle and identify the radius.

The graph of circle is

  

And the radius of circle is 5 units.

Given information:

Given equation of circle is:

  $x^2+y^2=25$

Formula used:

Standard form of equation of a circle with radius ‘ r’ and center $\left(h,k\right)$ is

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

Calculation:

In order to graph the given equation of circle

  $x^2+y^2=25$ ,

first identify it’s radius and center by comparing the equation with standard form of the equation of the circle:

  ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ , with radius ‘ r’ and center $\left(h,k\right)$ .

Rewrite the given equation as:

  $\begin{array}{c}{x}^2+y^2=25\\ {\left(x-0\right)}^2+{\left(y-0\right)}^2=5^2\end{array}$

Comparing above with ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ gives

  $\left(h,k\right)=\left(0,0\right)\text{ and }r=5$

Thus, the given circle has center at origin and has radius of units 5.

Thus, the graph will be as

  

And the radius of circle is 5 units.