Chapter 11.1, Problem 72E

To determine

Sketch the graph of the equation and the specified trace.

Answer to Problem 72E

The sphere of the equation $x^2+{(y+3)}^2+z^2=25$ and its intersection ${(y+3)}^2+z^2=5^2$

Explanation of Solution

Given:

Consider the following equation

  $x^2+{(y+3)}^2+z^2=25$

To find the $yz-$ trace of this surface, substitute $x=0$ in the equation,

  $x^2+{(y+3)}^2+z^2=25$

Put $x=0$

  $\begin{array}{cc}0+{(y+3)}^2+z^2& =25\\ {(y+3)}^2+z^2& =25\end{array}$

The equation ${(y+3)}^2+z^2=5^2$ is representing the intersection of the surface with the $yz$ plane.

The $yz-$ trace is a circle of radius $5$

The sphere of the equation $x^2+{(y+3)}^2+z^2=25$ and its intersection ${(y+3)}^2+z^2=5^2$ with

the $yz$ plane is shown in the graph