Question 143161
Use the midpoint formulas to calculate the coordinates of the diameter midpoint.  This will be the center of the circle, (h, k).  Use the distance formula to calculate the distance from one of the diameter endpoints to the center you just calculated, this will be the radius, r.


Midpoint formulas:


{{{x[m]=h=(x[1]+x[2])/2}}}, and {{{y[m]=k=(y[1]+y[2])/2}}}, giving you a circle center of <b><big> ({{{h}}},{{{k}}}) </b></big>.


Distance formula:


{{{r=sqrt((x[1]-h)^2+(y[1]-k)^2)}}}


Once you have <b><big> ({{{h}}},{{{k}}}) </b></big> and {{{r}}}, substitute into {{{(x-h)^2+(y-k)^2=r^2}}} and you will have your equation.


<b><big>Hint:</b></big> Pay close attention to your signs.