Determine the equation of the circle graphed below.
x
y
x
y
Center (2, -5)
(5, -2)
The equation of a circle with center (h, k) and radius r is given by:
(x - h)^2 + (y - k)^2 = r^2
Using the coordinates of the center (2, -5), the equation becomes:
(x - 2)^2 + (y + 5)^2 = r^2
To find the radius of the circle, we can use the distance formula between the center (2, -5) and a point on the circle (5, -2):
r = sqrt((5 - 2)^2 + (-2 - (-5))^2)
r = sqrt(3^2 + 3^2)
r = sqrt(18)
Therefore, the equation of the circle is:
(x - 2)^2 + (y + 5)^2 = 18