Question

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

Answer 1

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~ :)