Chapter 8.6, Problem 8E

Solution

Graph the given equation and identify the important characteristics of graph.

The graph of the given equation is

  

Thus, the radius of circle is 8 units with centre $\left(5,-1\right)$ .

Given information:

Given equation is:

  ${\left(x-5\right)}^2+{\left(y+1\right)}^2=64$

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:

The given equation can be rewritten as

  ${\left(x-5\right)}^2+{\left(y-\left(-1\right)\right)}^2={\left(8\right)}^2$

In order to graph the given equation

  ${\left(x-5\right)}^2+{\left(y-\left(-1\right)\right)}^2={\left(8\right)}^2$ ,

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 centre $\left(h,k\right)$ .

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

  $\left(h,k\right)=\left(5,-1\right)\text{ and }r=8$

Thus, the given circle has centre at $\left(5,-1\right)$ and has radius of 8 units.

Thus, the graph of this circle will be as

  

Thus, the radius of circle is 8 units with centre $\left(5,-1\right)$ .