SOLUTION: What would be the eqaution of a circle containging the points (0,-2) and (6,6) and whose center is on the line x - y = 1?

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Question 456905: What would be the eqaution of a circle containging the points (0,-2) and (6,6) and whose center is on the line x - y = 1?
Answer by spacesurfer(12) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of the line is y+=+x-1 rewritten. Hence a point on the line is (x, x-1). Let's say the center is at (x, x-1). Then the distance between (6,6) and the center = radius = distance between center and (0,-2). Using the point to point distance formula, we have
sqrt%28%28x-6%29%5E2+%2B+%28x-1-6%29%5E2%29+=+sqrt%28x%5E2%2B%28x-1%2B2%29%5E2%29
This is the same as %28x-6%29%5E2%2B%28x-7%29%5E2+=+x%5E2+%2B+%28x%2B1%29%5E2
The solution is x = 3. Hence, the center is at (3,2).
The radius = 5 since sqrt%28%286-3%29%5E2+%2B+%286-2%29%5E2%29+=+5.
So, the equation of the circle is %28x-3%29%5E2+%2B+%28y-2%29%5E2+=+5%5E2