Question

(a) Find the center and radius, then (b) graph the circle: $x^2+y^2-6x-8y+9=0$

Short answer

The center and the radius of the circle are $(3,4)$ and $4$respectively. The graph of this circle is:

Step-by-step solution

Part (a) Step 1. Given information.

The equation of the circle is$x^2+y^2-6x-8y+9=0$

We have to find radius and center.

Also, we have to graph this circle.

Part (a) Step 2. Complete the squares

Collect the x- and y- terms,

$$\begin{gathered} x^2+y^2-6x-8y+9=0 \\ {x}^2-6x+y^2-8y=-9 \\ {x}^2-6x+9+y^2-8y+16=-9+9+16 \\ {(x-3)}^2+{(y-4)}^2=16 \end{gathered}$$

Part (a) Step 3. Compare with the standard form of a circle to find radius and center 

Compare ${(x-3)}^2+{(y-4)}^2=16$with role="math" localid="1645268784417" ${(x-h)}^2+{(y-k)}^2=r^2$

We have, $(h,k)=(3,4)$(centre)

and$r=4$(radius)

Part (b) Step 1. Graph the circle

The graph is: