Answer:
(x - 1)^2 + (y + 4)^2 = 5^2
Step-by-step explanation:
Find the length of the diameter and then halve the result to find the radius.
Finding the diameter involves using the Pythagorean Theorem:
6^2 + 8^2 = 36 + 64 = 100, and so the diameter is √100, or 10. Thus, the radius is half that, or 5.
Next we find the coordinates of the center, (h, k). Using the midpoint formula is a fast way in which to do that:
-2 + 4 2 - 10
xmidpoint = ------------- = 1, and ymidpoint = ----------- = -4
2 2
Then the center of the circle is (1, -4) and the radius is 5.
Using the standard equation of a circle centered at (h, k) and with radius 5,
(x - h)^2 + (y - k)^2 = r^2 becomes
(x - 1)^2 + (y + 4)^2 = 5^2