Question 730942
The standard equation of a circle with center C({{{h}}},{{{k}}}) and radius {{{r}}} is as follows:

{{{(x-h)^2 + (y -k)^2 = r^2}}}

so, we need to find {{{h}}},{{{ k}}}, and {{{r}}}

since the circle that contains P and Q , the distance between them is equal to diameter of the circle:

*[invoke distance_formula -3, 6, 10, 1]

so, diameter {{{d=13.9}}}...=>...{{{r=13.9/2}}}...=>...{{{r=6.95}}}

now find midpoint:

*[invoke midpoint -3, 6, 10, 1]

center is ({{{3.5}}}, {{{3.5}}})=({{{h}}},{{{ k}}})...so {{{h=3.5}}} and {{{k=3.5}}}

{{{(x-h)^2 + (y -k)^2 = r^2}}}...plug in {{{h=3.5}}},{{{k=3.5}}}, and {{{r=6.95}}}

your equation is:


{{{(x-3.5)^2 + (y -3.5)^2 = 6.95^2}}}


{{{ drawing ( 400, 400, -5, 15, -5, 15, circle(3.5,3.5,6.95),circle(3.5,3.5,0.1),graph( 400, 400,  -5, 15, -5, 15, 0 ) )}}}