help

Hello wiseowl! 

The diameter must pass through the midpoint of the circle. Furthermore, the midpoint of the diameter is the center of the circle. 

Therefore, from the diameter, we can find the radius length and center, finding the equation in the end. 

The midpoint of (-1,-3) and (5,1) is \((\frac{-1+5}{2},\frac{-3+1}{2})\) or \((2,-1)\).

The diameter length is \(\sqrt{(5-(-1))^2+(1-(-3))^2}=2\sqrt{13}\)

Then the radius must be \(\sqrt{13}\)

The equation of the circle must be \((x-2)^2+(y+1)^2=13\)

I hope this helped, 

Gavin