SOLUTION: Find the center and the radius of the circle that passes through the points (4,4) , (1,3) and (8,-4). What are the coordinates of the center? Thank you in advanced.

Question 985229: Find the center and the radius of the circle that passes through the points (4,4) , (1,3) and (8,-4).
What are the coordinates of the center?
Thank you in advanced.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Find the center and the radius of the circle that passes through the points
(,) , (,) and (,).

equation of the circle is:
where and are and coordinates of the center, and is radius
so use given points to set up system of three unknown
(,)
....simplify
.............eq.1
(,)

.............eq.2

(,)
....simplify
.............eq.3
start with
.............eq.1
.............eq.3
--------------------------------------------------------------------subtract

.......both sides divide by 8

...............eg.1a

go with
.............eq.1
.............eq.2
---------------------------------------------------------subtract

...............eg.2a
now go with
...............eg.1a
...............eg.2a
-----------------------------------------------subtract

go to
...............eg.1a...plug in for

go to
.............eq.1 ..plug in for and for and find

so, your equation is:

check:

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