Chapter 9, Problem 3CR

To determine

The equation for the circle with center $\left(0,1\right)$ and radius $3$ , also graph the circle.

Answer to Problem 3CR

Solution:

The equation of circle is $x^2+{\left(y-1\right)}^2=9$ and graph of circle as:

  

Explanation of Solution

Given information:

The center $\left(0,1\right)$ and radius $3$ .

To find the equation of circle with center $\left(0,1\right)$ and radius $3$ ,

The general equation of circle with center $\left(a,b\right)$ and radius $r$ is ${\left(x-a\right)}^2+{\left(y-b\right)}^2=r^2$ .

Here, center $\left(0,1\right)$ and radius $3$ .

Substituting the value of $\left(a,b\right)=\left(0,1\right)$ and $r=3$ .

  ${\left(x-0\right)}^2+{\left(y-1\right)}^2=3^2$

  $\Rightarrow {\left(x\right)}^2+{\left(y-1\right)}^2=9$

The required equation of circle with center $\left(0,1\right)$ and radius $3$ is $x^2+{\left(y-1\right)}^2=9$ .

The graph of circle $x^2+{\left(y-1\right)}^2=9$ is as shown in below: