Question 974016: Find the equation of the circle whose center lies on the line y=3x-7 and which passes through the points (1,1) and (2,-1). Express the answer in x^2+y^2+Ax+By+C=0. Please show steps as well. These problems bug me.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! The line is the general point (x,3x-7).
This will yield values for x for the center.
Both sides contain terms x^2 and 9x^2...
Use the given line containing the center of the circle to find the y value:
The center of the circle is ( 5/2, 1/2 ).
Use the Distance Formula again to find the radius, which is distance from ( 5/2, 1/2 ) to either of the given points. You should do that on your own. Once you have that value, then use standard form for a circle, and convert into the general form you want. It would be starting like this:
 , and you will want the finished form to use, if possible, integer coefficients.
maybe also to
 , but again, you need to compute r or r^2 in order to finish.
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