Determine the equation of the circle whose circumference is 14*pi and the center is (3,-2).

Given the circumference of a circle is 14pi and the center
is at the point (3,-2).

We need to determine the equation
of the circle.

First, we need to write into the standard
form of the circle:

(x-a)^2 + ( y-b)^2 =r^2 where (a,b) is
the center and r is the radius.

==> (x-3)^2 + (
y+2)^2 = r^2.

Now we need to find the radius of the
circle.

Given the circumference C =
14pi.

==> 2*r*pi =
14pi

==? r= 14pi/ 2pi = 7

Then
the radius of the circle is 7.

==> (x-3)^2 + ( y+2)
= 7^2

==> (x-3)^2 + ( y+2)^2 =
49