SOLUTION: Write an equation for the circle with the endpoints of the diameter at (-6,4) and (4,8)

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Question 751709: Write an equation for the circle with the endpoints of the diameter at (-6,4) and (4,8)
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
First, get the length of the diameter by computing the
distance between the points (-6, 4) and (4, 8).
Using the distance formula:
d = sqrt%28%288+-+4%29%5E2+%2B+%284+-+%28-6%29%29%5E2%29%29
= sqrt%28116%29
= 2sqrt%2829%29
The length of the radius is half the length of the diameter.
r = %281%2F2%29%28d%29 = sqrt%2829%29.
Next, we get the coordinates of the center of the circle by
computing the midpoint of the diameter with endpoints (-6,4) and (4,8).
Using the midpoint formula:
center = (%28-6+%2B+4%29%2F2, %284+%2B+8%29%2F2)
= (-1, 6)
The equation of the circle with center (h,k) and radius r is
%28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2, the center is (h,k) = (-1,6) and radius, r = sqrt%2829%29
Equation: highlight%28%28x+%2B+1%29%5E2+%2B+%28y+-+6%29%5E2+=+29%29