Chapter 9.2, Problem 11WE

To determine

To graph: Plot the graph for the given equation.

Explanation of Solution

Given information: It is given that ${\left(x-4\right)}^2+{\left(y-5\right)}^2=1$ .

Calculation: Let a circle has the center $\left(h,k\right)$ and radius of $r$ then the equation of the circle is ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$ .

Compare the given equation to ${\left(x-h\right)}^2+{\left(y-k\right)}^2=r^2$

Hence,

  $\left(h,k\right)=\left(4,5\right)$ and $r=\sqrt{1}=1$

Graph: The required graph is given below.

  

Interpretation: The circle’s points are equidistant from a fixed point $\left(4,5\right)$ . And its radius is 1.