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Question 1190993: Find the equation of a circle that has a diameter with the endpoints given by the points A (2, -2) and B (-3, 3).
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
The x coordinates of points A and B are 2 and -3 respectively.
Add up the x values: 2 + (-3) = -1
Then cut that result in half: -1/2 = -0.5
The x coordinate of the midpoint is x = -0.5
Repeat for the y coordinate of the midpoint.
Add: -2+3 = 1
Cut in half: 1/2 = 0.5
The y coordinate of the midpoint is y = 0.5
The midpoint of segment AB is (-0.5, 0.5)
This means (h,k) = (-0.5, 0.5) is the center of the circle, since AB is a diameter.
In fraction form that would be (h,k) = (-1/2, 1/2)
Let's label this point C.
To get the radius, find the distance from A to C.
We'll use the aptly named distance formula.
A = (x1,y1) = (2,-2) and C = (x2, y2) = (-0.5, 0.5)
^2 + (y_1 - y_2)^2})
)^2 + (-2-0.5)^2})
^2 + (-2-0.5)^2})
^2 + (-2.5)^2})
The exact length of segment AC is 
This means the radius is 
Squaring both sides gets us 
So we have
^2 + (y-k)^2 = r^2)
)^2 + (y-0.5)^2 = 12.5)
^2 + (y-0.5)^2 = 12.5)
which is the equation of the circle.
Optionally you can replace each 0.5 with 1/2, and you can replace 12.5 with the improper fraction 25/2
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