Question 1041238: Find the center of the circle with points (-7,0) , (-3,4) , and (7,0).
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! Part of an explanation on " Ask Dr. Math" says:
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"Let the equation of the circle be
(x-h)^2 + (y-k)^2 = r^2,
and substitute the three known points, getting 3 equations in 3
unknowns h, k, and r:
(x1-h)^2 + (y1-k)^2 = r^2
(x2-h)^2 + (y2-k)^2 = r^2
(x3-h)^2 + (y3-k)^2 = r^2 "
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(-7,0)
(-3,4)
( 7, 0)
These points give me the equations:
(1) 
(2) 
(3) 
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From (1) and (3), I get:
(3) 
(3) 
(3) 
(3) 
(3) 
(3) 
(3) 
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Plug this result into (2)
(2) 
(2) 
(2) 
(2) 
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From (3):
(3) 
(3) 
and, plugging into (2)
(2) 
(2) 
(2) 
(2) 
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The center is at ( 0, -3 )
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check:
(3)
(3) 
(3) 
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The equation is:
Plug in (-7,0)
OK
Plug in (-3,4)
OK
plug in (7,0)
OK
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