Question 319456: Find the co ordinate of the centre of a circle which passes through the points A(1,2),B(3,-4) and C(5,-6).Also find the radius of the circle.
Answer by Greenfinch(383)   (Show Source):
You can put this solution on YOUR website! Chord AB has gradient -6/2 or -3. Chord AC has gradient -8/4 or -2
Perpendicular lines therefore have gradients of 1/2 and 1/3 respectively.
The perpendicular will go through the mid point of the chord or (2,-1) and (3,-2)
The line going through(2,-1) with a gradient of 1/3 is y=1/3x -5/3
The line going through (3,-2) with a gradient of 1/2 is y = 1/2x - 7/2
re-arrange to 3y - x = 5 and 2y - x = 7
Solve simultaneously to get y = 2, which gives x = 11
So centre of circle is (11,2).
Point A is on the circumference, so the radius is (1,2) to (11,2) or 10.
The equation or the circle is thus (y - 2)^2 + (x - 11)^2 = 100
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