circle has a center at (-8,-4) and circumference of 32.determine equation of the circle

recall that the equation of a circle is given by

(x-h)^2 + (y-k)^2 = r^2
where
h = x-coordinate of the center
k = y-coordinate of the center
r = radius
since in the problem, the center lies at (-8, -4) we have
h = -8
k = -4
also, we need to solve for the radius from the circumference
recall that circumference of a circle is just 2*pi*r
therefore,
32 = 2*pi*r
r = 32/(2*pi) = 5.096
substituting to the general equation of a circle,
(x + 8)^2 + (y + 4)^2 = (5.096)^2
(x + 8)^2 + (y + 4)^2 = 25.96

hope this helps~ :)

To determine the equation of a circle, we need to use the formula for the equation of a circle:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) represents the coordinates of the center of the circle and r represents the radius of the circle.

In this case, we are given that the center of the circle is at (-8, -4) and the circumference of the circle is 32.

To find the radius, we need to use the formula for the circumference of a circle:

C = 2πr

Given that the circumference is 32, we can solve for the radius:

32 = 2πr
r = 32 / (2π)
r = 16 / π

Now that we have the radius, we can plug it into the equation of the circle formula:

(x - (-8))^2 + (y - (-4))^2 = (16 / π)^2

Simplifying further:

(x + 8)^2 + (y + 4)^2 = 256 / π^2

Therefore, the equation of the circle is:

(x + 8)^2 + (y + 4)^2 = 256 / π^2