SOLUTION: Find an equation of the circle whose diameter has endpoints (-1,4) and (4,2)

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Question 1057344: Find an equation of the circle whose diameter has endpoints (-1,4) and (4,2)
Found 2 solutions by Fombitz, math_helper:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the midpoint of the line connecting the two endpoints.
That's the center of the circle.
Find the length of the line connecting the two endpoints.
That's the diameter of the circle.
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Midpoint:
x%5Bm%5D=%28-1%2B4%29%2F2=3%2F2
y%5Bm%5D=%284%2B2%29%2F2=3
Distance:
D%5E2=%28-1-4%29%5E2%2B%284-2%29%5E2
D%5E2=%28-5%29%5E2%2B%282%29%5E2
D%5E2=25%2B4
D%5E2=29
D=sqrt%2829%29
R=sqrt%2829%29%2F2
So then the equation of the circle is,
%28x-3%2F2%29%5E2%2B%28y-3%29%5E2=29%2F4
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Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
The general form of a circle with center at (h,k) is:
+%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2+
So we need to find the center and the radius.
If the endpoints of the diameter are (-1,4) and (4,2) then the center is at
the midpoint of those: ( (-1+4)/2, (4+2)/2 ) or (3/2, 3)
The radius is just half the diameter:
+%281%2F2%29sqrt%28%28-1-4%29%5E2+%2B+%284-2%29%5E2%29+
= +%281%2F2%29sqrt%2825+%2B+4%29+
= +sqrt%2829%29%2F2+

So the equation of the circle is:
++%28x-3%2F2%29%5E2+%2B++%28y-3%29%5E2++=++%2829%2F4%29+