Posted by kyle on Saturday, January 15, 2011 at 4:20pm.
DETERMINE the equation of the circle that has the following three points on its circumference: A(1,5), B(3,7) and C(5,5).

Math  Damon, Saturday, January 15, 2011 at 5:07pm
(xk)^2+ (yh)^2 = r^2
so
(1k)^2 + (5h)^2 = r^2
(3k)^2 + (7h)^2 = r^2
(5k)^2 + (5h)^2 = r^2
Now before I go off and solve those for k,h and r, sketch a graph
Notice that two points, A and C are at the same height,5
The third point,B, is half way between them (3 is halfway between 1 and 5)
I conclude that the center of the circle is on x = 3
so
k = 3
Onward
(13)^2 + (5h)^2 = r^2
(33)^2 + (7h)^2 = r^2
(53)^2 + (5h)^2 = r^2
that second equation is pretty easy now.
(7h)^2 = r^2
the first and third are actually the same now that we know what k isso use the first and the second
4 + (5h)^2 = r^2
(7h)^2 = r^2
29  10 h + h^2 = r^2
49 14 h + h^2 = r^2

20 +4 h = 0
h = 5
well I guess you can take it from there

Math  kyle, Saturday, January 15, 2011 at 5:33pm
Thank you!
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