Chapter 9.3, Problem 59PPS

To determine

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

Answer to Problem 59PPS

  $\begin{array}{l}(h,k)=\left(0,-\frac{9}{2}\right)\\ r=\sqrt{19}\end{array}$

Explanation of Solution

Given: $4x^2+4y^2+36y+5=0$

Equation of the circle

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

We can write the equation $4x^2+4y^2+36y+5=0$ as

  $\begin{array}{l}4x^2+4y^2+36y+5=0\\ x^2+{\left(y+\frac{9}{2}\right)}^2=19\\ x^2+{\left(y+\frac{9}{2}\right)}^2={\left(\sqrt{19}\right)}^2\end{array}$

Comparing with $(i)$

We get

  $\begin{array}{l}(h,k)=\left(0,-\frac{9}{2}\right)\\ r=\sqrt{19}\end{array}$

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

The graph of the circle is