Question 800398
If those are the endpoints of the diameter, then Midpoint Formula will give the coordinates for the center of the circle.  You could then choose either given point and use the distance formula to calculate the radius of the circle.


Now, just plug the needed and found values into the Standard Form equation for a circle.


{{{x=(5-3)/2=1}}}
{{{y=(1+3)/2=2}}}
Center of Diameter is (1,2) meaning this is the center of the circle.


Radius:  {{{sqrt((5-1)^2+(1-2)^2)=sqrt(4^2+(-1)^2)=sqrt(17)}}}


Using knowledge of standard form for a circle,
{{{highlight((x-1)^2+(y-2)^2=17)}}}