Question

In the following exercises, ⓐ find the center and radius, then ⓑ graph each circle.

${(x-1)}^2+{(y-3)}^2=\frac{9}{4}$

Short answer

(a) Center of the circle ${(x-1)}^2+{(y-3)}^2=\frac{9}{4}$is $(1,3)$and radius is $1.5$

(b) graph of the circle is

Step-by-step solution

Step 1. given data

The given equation of the circle is

${(x-1)}^2+{(y-3)}^2=\frac{9}{4}$

Step 2. Part (a)

Compare the equation of the circle with the standard equation of the circle

$$\begin{gathered} {(x-1)}^2+{(y-3)}^2=\frac{9}{4} \\ {(x-1)}^2+{(y-3)}^2={\left(\frac{3}{2}\right)}^2 \\ {(x-1)}^2+{(y-3)}^2={\left(1.5\right)}^2 \\ {(x-h)}^2+{(y-k)}^2={\left(r\right)}^2 \end{gathered}$$

so center$(h,k)=(1,3)$

and radius$r=1.5$

Step 3. Part (b)

Plot the circle of center $(1,3)$and radius $1.5$