Chapter 9.3, Problem 42PPS

To determine

To Find: The center and radius of the circle then graph the circle.

Answer to Problem 42PPS

  $\begin{array}{l}(h,k)=\left(\frac{3}{2},-4\right)\\ r=\frac{3\sqrt{17}}{2}\end{array}$

Explanation of Solution

Given: $x^2+y^2-3x+8y=20$

Equation of the circle

  ${(x-h)}^2+{(y-k)}^2=r^2\mathrm{....}(i)$

We can write the equation $x^2+y^2-3x+8y=20$ as

  $\begin{array}{}$ x^2+y^2-3x+8y=20$$ {\left(x-\frac{3}{2}\right)}^2+{(y-(-4))}^2={\left(\frac{3\sqrt{17}}{2}\right)}^2$$ {\left(x-\frac{3}{2}\right)}^2+{(y+4)}^2={\left(\frac{3\sqrt{17}}{2}\right)}^2$\end{array}$

Comparing with $(i)$

We get

  $\begin{array}{l}(h,k)=\left(\frac{3}{2},-4\right)\\ r=\frac{3\sqrt{17}}{2}\end{array}$

Where $(h,k)$ is the center of the circle and $r$ is the radius of the circle

The graph of the circle is