SOLUTION: Find an equation of the circle whose diameter has endpoints (-5,-5) and (3,1)

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Question 1134505: Find an equation of the circle whose diameter has endpoints (-5,-5) and (3,1)

Found 2 solutions by mathsolverplus, josmiceli:
Answer by mathsolverplus(88) About Me  (Show Source):
You can put this solution on YOUR website!
Find the distance between the two points first:
d=sqrt%28%281-%28-5%29%29%5E2%2B%283-%28-5%29%29%5E2%29
d=sqrt%2836%2B64%29
d=10
If diameter = 10, radius = 5 because radius is half of diameter.
Now, we need to find the center of the circle, which is midpoint between the two given points.
Midpoint = ((-5+3)/2, (-5+1)/2)
= (-1, -2)
The equation of a circle:
%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 (h,k) is the center and r = 5
We found center to be (-1,-2) and radius = 5:
Solution: %28x%2B1%29%5E2%2B%28y%2B2%29%5E2=25


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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Find the center of the endpoints
+h+=+%28+-5+%2B+3+%29%2F2+
+h+=+-2%2F2+
+h+=+-1+
and
+k+=+%28+-5+%2B+1+%29%2F2+
+k+=+-4%2F2+
+k+=+-2+
---------------------------
The center is at ( -1, -2 )
+%28+x+-+h+%292+%2B+%28+y+-+k+%29%5E2+=+r%5E2+
-----------------------------------
Find the length of the radius
+d%5E2+=+%28+3+-%28-5%29+%29%5E2+%2B+%28+1+-%28-5%29+%29%5E2+
+d%5E2+=+64+%2B+36+
+d%5E2+=+100+
+d+=+10+
+r+=+5+
--------------------
+%28+x+-%28-1%29+%29%5E2+%2B+%28+y+-%28-2%29+%29%5E2+=+5%5E2+
+%28+x+%2B+1+%29%5E2+%2B+%28+y+%2B+2+%29%5E2+=+25+
-----------------------------------------
check:
( -5,-5 )
+%28+-5+%2B+1+%29%5E2+%2B+%28+-5+%2B+2+%29%5E2+=+25+
+16+%2B+9++=+25+
OK
( 3,1 )
+%28+3+%2B+1+%29%5E2+%2B+%28+1+%2B+2+%29%5E2+=+25+
+16+%2B+9+=+25+
OK