Chapter 8.3, Problem 15Q

Solution

Graph the given equation of circle and identify the radius.

The graph of circle is

  

And the radius of circle is $2\sqrt{5}$ units.

Given information:

Given equation of circle is:

  $x^2+y^2=20$

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

  $x^2+y^2=20$ ,

first identify its 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:

  $\begin{array}{c}{x}^2+y^2=20\\ {\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(\sqrt{20}\right)}^2\\ {\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(2\sqrt{5}\right)}^2\end{array}$

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

  $\left(h,k\right)=\left(0,0\right)\text{ and }r=2\sqrt{5}$

Thus, the given circle has center at origin and has radius of units $2\sqrt{5}$ .

Thus, the graph will be as

  

And the radius of circle is $2\sqrt{5}$ units.