SOLUTION: Find the co-ordinate of the center of a circle which passes through the points A(1,2),B(3,-4)& C(5,-6).Also find the radius of the circle.

Question 319390: Find the co-ordinate of the center of a circle which passes through the points A(1,2),B(3,-4)& C(5,-6).Also find the radius of the circle.
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the perpendicular bisector of a chord of a circle passes through the center

the intersection of two PB's defines the center

the midpoint of chord AB is (2,-1)
___ the slope of AB is -6/2 or -3 , so the slope of the PB is 1/3
___ the equation of the PB (using point-slope) is ___ y + 1 = (1/3)(x - 2)
___ 3y = x - 5

the midpoint of chord BC is (4,-5)
___ the slope of BC is -2/2 or -1 , so the slope of the PB is 1
___ the equation of the PB (using point-slope) is ___ y + 5 = (1)(x - 4)
___ y = x - 9

substituting ___ 3(x - 9) = x - 5 ___ 3x - 27 = x - 5 ___ x = 11

substituting ___ y = (11) - 9 = 2

so the center is (11,2)

looking at point A , the radius is 10

FYI ___ the equation of the circle is ___ (x - 11)^2 + (y - 2)^2 = 100
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