Question 850088
{{{graph(300,300,-10,10,-10,10,7-sqrt(.2^2-(x-3)^2),5+sqrt(.2^2-(x-5)^2),x/4-1/4)}}}


The center of the circle is some unknown point on the blue line, and the small almost stray-like marks are the locations of the given points to be contained on the circle.  


The points on the line are variables in the form of ordered pairs, (x, x/4-1/4).  All points on a circle are equidistant from the center, so we can apply the distance formula for this center and each of the given circle's points.


{{{sqrt((x-3)^2+(x/4-1/4-7)^2)=sqrt((x-5)^2+(x/4-1/4-5)^2)}}}
and expect from this to perform some algebraic steps to reach a solution for x, and then just use it to compute y; and you have the center point for the circle.    The steps are omitted here because of the time length to type in all the text.  
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Result is x=-3, and y=-1; for the center of (-3,-1).
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The radius for the circle can now be found using this found center point and either of the given points.
radius, {{{r=sqrt((-3-5)^2+(-1-5)^2)=sqrt(64+36)=sqrt(100)=10}}}
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The circle's equation is {{{highlight((x+3)^2+(y+1)^2=10^2)}}}.