We use the general equation of a circle to compare it with the equation given by the problem, then find the radius of the circle, and then the circumference.
Step 1. The general equation of a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) are the coordinates of the center of the circle (we are not using this in the problem) and r is the radius of the circle.
And the equation given in the problem is:
[tex](x-9)^2+(y-3)^2=64[/tex]
By comparison, we can see that:
[tex]r^2=64[/tex]
Step 2. Find the radius of the circle.
In the last step we got the equation:
[tex]r^2=64[/tex]
To solve for r, we take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{r^2}=\sqrt[]{64} \\ r=\sqrt[]{64} \\ r=8 \end{gathered}[/tex]
Step 3. Find the circumference of the circle.
We use the formula for the circumference "c":
[tex]c=2\pi r[/tex]
Substituting r=8:
[tex]\begin{gathered} c=2\pi(8) \\ c=16\pi \end{gathered}[/tex]
Answer:
16π
