Chapter 11.1, Problem 46SPR

To determine

To calculate: The equation of circle for the given information.

Answer to Problem 46SPR

The equation of the circle is $x^2+y^2=9$ .

Explanation of Solution

Given information: The center is at the origin (0,0) and the radius is $r=3$ .

Formula used:

The equation of a circle is given by

  $\begin{array}{l}{\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2\\ \left(h,k\right)\text{is}\text{the}\text{coordinates}\text{of}\text{the}\text{origin}\text{\&}r\text{is}\text{the}\text{radius}\text{of}\text{the}\text{circle}\text{.}\end{array}$

Calculation:

From the given information it can be observed that

  $\begin{array}{c}\left(h,k\right)=\left(0,0\right)\\ \&\\ r=3\end{array}$

The equation of the circle is

  $\begin{array}{l}{\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2\\ {\left(x-0\right)}^2+{\left(y-0\right)}^2={\left(3\right)}^2\\ x^2+y^2=9\end{array}$

Therefore the equation of the circle is $x^2+y^2=9$ .