Chapter 9.3, Problem 65HP

To determine

To Write: Two equations of the concentric circles and graph the equations.

Answer to Problem 65HP

  $\begin{array}{l}{(}^x+{(}^y=16\\ {(}^x+{(}^y=25\end{array}$

Explanation of Solution

Given: Concentric circles have the same center but not the same radius.

Equation of the circle

  ${(x-h)}^2+{(y-k)}^2=r^2$

Let

  $\begin{array}{l}(h,k)=(1,-1)\\ r_1=4\\ r_2=5\end{array}$

Then

Equations are

  $\begin{array}{}$ {(x-h)}^2+{(y-k)}^2=r^2$$ {(x-1)}^2+{(y+1)}^2=4^2$$ {(x-1)}^2+{(y+1)}^2=16\dots (i)$$ {(x-1)}^2+{(y+1)}^2=5^2$$ {(x-1)}^2+{(y+1)}^2=\mathrm{25..}(ii)$i.e.$ {(x-1)}^2+{(y+1)}^2=16$$ {(x-1)}^2+{(y+1)}^2=25$\end{array}$

The graph of the equations are