Chapter 9.1, Problem 113E

To determine

To find the error

Answer to Problem 113E

The error is to finding the radius, since the diameter is given equal to 4, it radius must be equal to 2.on comparing the standard form of equation it can be seen that the radius is 4

Explanation of Solution

Given information:

Circle; center $\left(0,3\right)$ , diameter: $4$

The equation is

  $x^2+{\left(y-3\right)}^2=16$

To observed the error

  $\begin{array}{l}{x}^2+{\left(y-3\right)}^2=16\\ x^2+{\left(y-3\right)}^2=4^2\end{array}$

The standard form of the equation of a circle is

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

Where $\left(h,k\right)$ is the center and $r$ is the radius.

Compare the given equation to the standard form of equation

  $h=0,k=3\text{ and }r=4$

Since,

  $\begin{array}{l}d=4\\ r\text{ = }\frac{4}{2}\left[\begin{array}{l}\text{d=diameter}\\ \text{r=radius}\end{array}\right]\\ r=2\\ \end{array}$

Hence,

The error is to finding the radius, since the diameter is given equal to 4, it radius must be equal to 2.on comparing the standard form of equation it can be seen that the radius is 4