SOLUTION: Find an equation of the circle whose diameter has endpoints (-5,6) and (-3,-4)

Question 672444: Find an equation of the circle whose diameter has endpoints (-5,6) and (-3,-4)
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
The center of the circle is in the "middle" of the diameter which is the average of the end points.
The x co-ordinant of the center of the circle is
(1) x = (-5 + -3)/2 or
(2) x = -4
The y co-ordinant of the center of the circle is
(3) y = (6 + (-4))/2 or
(4) y = 1
This gives us part of the circle equation as
(5) (x+4)^2 + (y-1)^2 = r^2
Now we need to find r. Let's get the diameter first by using
(6) d^2 = ((-3-(-5))^2 + (6 - (-4))^2 or
(7) d^2 = 2^2 + 10^2 or
(8) d^2 = 104.
Using d = 2r we get
(9) 4*r^2 = 104 or
(10) r^2 = 104/4 or
(11) r^2 = 26
The final equation of the circle is
(12) (x+4)^2 + (y-1)^2 = 26
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