SOLUTION: Find an equation of the circle passing through A(2,4), B(-2,6) and O(0,0)

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Question 1065346: Find an equation of the circle passing through A(2,4), B(-2,6) and O(0,0)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of OA is %284-0%29%2F%282-0%29=4%2F2=2 .
The slope of AB is %284-6%29%2F%282-%28-2%29%29=%28-2%29%2F%282%2B2%29=%28-2%29%2F4=-1%2F2 .
Since the product of the slopes is
2%2A%28-1%2F2%29=-1 , OA and AB are perpendicular.
Angle OAB is an inscribed right angle in the circle we are looking for,
OB is a diameter of that circle,
and the center of the circle is the midpoint of OB,
C%28-1%2C3%29 .
OB%5E2=%28-2%29%5E2%2B6%5E2=4%2B36=40=diameter%5E2=%282radius%29%5E2=4%2Aradius%5E2
So radius%5E2=40%2F4=10
With C%28-1%2C3%29 and radius%5E2=10 ,
we can write the equation for the circle as
%28x%2B1%29%5E2%2B%28y-3%29%5E2=10 .