Find an equation of the circle that has center (-1, - 3) and passes through (3, 2).
To find the equation of a circle given its center and a point on the circle, we can use the general equation for a circle:
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) is the center of the circle and r is the radius of the circle.
In this case, the center of the circle is (-1, -3) and a point on the circle is (3, 2). Using the distance formula, we can find the radius of the circle:
r = sqrt((3 - (-1))^2 + (2 - (-3))^2)
r = sqrt(16 + 25)
r = sqrt(41)
So, the equation of the circle is:
(x + 1)^2 + (y + 3)^2 = 41