Circle o, with center (x, y), passes through the points a(0, 0), b(–3, 0), and c(1, 2). find the coordinates of the center of the circle.

Since we are given three points on the circle, and we know that each point is a distance equal to the radius to some point (x,y), we can set up a system of equations to solve for the center...

Knowing that the distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2 and these distances are all equal we can say

d^2=(x-0)^2+(y-0)^2, (x+3)^2+(y-0)^2, (x-1)^2+(y-2)^2

d^2=x^2+y^2,  x^2+6x+9+y^2,  x^2-2x+1+y^2-4y+4  now getting differences

0=-6x-9,  8x+4+4y  

Since both of the equations above are equal to zero we can see that:

-6x-9=0

-6x=9

x=-9/6

x=-1.5, making 8x+4+4y=0 become:

8(-1.5)+4+4y=0

-12+4+4y=0

-8+4y=0

4y=8

y=2

So the center of this circle is at the point (-1.5, 2)

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