Question 730942: Let P(-3,6) and Q(10,1) be two points in the coordinate plane
Find an equation of the circle that contains P and Q and whose center is the midpoint of the segment PQ
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! The standard equation of a circle with center C( , ) and radius  is as follows:
so, we need to find , , and
since the circle that contains P and Q , the distance between them is equal to diameter of the circle:
| Solved by pluggable solver: Distance Formula |
The first point is (x1,y1). The second point is (x2,y2)
Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
So  , 
Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
So  , 
Put this all together to get: , , , and
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Now use the distance formula to find the distance between the two points (-3, 6) and (10, 1)
 Plug in , , , and
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Answer:
The distance between the two points (-3, 6) and (10, 1) is exactly  units
The approximate distance between the two points is about 13.9283882771841 units
So again,
Exact Distance: units
Approximate Distance:  units
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so, diameter  ...=>... ...=>...
now find midpoint:
| Solved by pluggable solver: Midpoint |
The first point is (x1,y1). The second point is (x2,y2)
Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6)
So ,
Since the second point is (10, 1), we can also say (x2, y2) = (10, 1)
So ,
Put this all together to get: , , , and
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Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2
X Coordinate of Midpoint = 
X Coordinate of Midpoint = 
X Coordinate of Midpoint = 
X Coordinate of Midpoint = 
So the x coordinate of the midpoint is 3.5
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Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2
Y Coordinate of Midpoint = 
Y Coordinate of Midpoint = 
Y Coordinate of Midpoint =
Y Coordinate of Midpoint =
So the y coordinate of the midpoint is 3.5
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Summary:
The midpoint of the segment joining the two points (-3, 6) and (10, 1) is (3.5, 3.5).
So the answer is (3.5, 3.5)
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center is (, )=(,)...so  and 
...plug in ,, and
your equation is:
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