Chapter 11.3, Problem 10E

To determine

Tosketch:The set of points whose polar coordinates satisfy the equation $r^2+8=6r$ .

Answer to Problem 10E

The graph is two concentric circle with radius 2 and 4.

Explanation of Solution

Given information:

The equation $r^2+8=6r$

Graph:

Given equation is $r^2+8=6r$ .

Solve the equation

  $\begin{array}{c}{r}^2+8=6r\\ r^2-6r+8=0\\ r^2-4r-2r+8=0\\ r\left(r-4\right)-2\left(r-4\right)=0\\ \left(r-2\right)\left(r-4\right)=0\end{array}$

  $\therefore r=2\text{or}r=4$

Now, draw all the points with distance 2and 4 from the origin. Which form two circle.

  

Conclusion:

Hence, the graph is two concentric circle with radius 2 and 4.