This circle passes through the points (-1, 2), (3,0) and (9,0). The center of the circle is at (h,k). What is the value of h+k?

 May 31, 2020

Call the points:  A = (-1,2)    B = (3,0)     and    C = (9,0).


The idea behind this problem is this:  the perpendicular bisectors of the chords intersect at the center.


For chord AB.

1)  Find the midpoint of this chord.

2)  Find the slope of this chord

3)  Use this slope to find the slope of the line perpendicular to this chord.

4)  Find the equation of the perpendicular bisector of this chord by using the point from step 1 and the slope from step 3.


Now, follow the same steps for chord BC or chord AC (your choice).


Then, use the two equations to find their point of intersection; this is the center of the circle.

 May 31, 2020

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