Answer:
(x + 3)^2 + (y - 4)^2 = 5
Explanation:
Note that the center is the midpoint of the diameter. Use the midpoint formula to find the coordinates of the center:
-8 + 2
x0 = ----------- = -3
2
6 + 2
y0 = ----------- = 4
2
The center of this circle is (-3, 4).
Thus, the equation of this circle is (x + 3)^2 + (y - 4)^2 = r^2.
Find r by substituting the coordinates of one of the diameter endpoints into the above equation:
(-2 + 3)^2 + (6 - 4)^2 = r^2, or
1 + 4 = r^2 = 5. Thus, the radius is √5.
The fourth answer choice best corresponds with the above result.
The equation of the circle is either the generic (x + 3)^2 + (y - 4)^2 = r^2 or the specific (x + 3)^2 + (y - 4)^2 = 5.