The equation x^2+y^2-2x+2y-1=0 is the general form of a circle. what is the center and radius of this circle

You have to rewrite the general form to the binomial form
(x-1)^2=x^2-2x+1
(y+1)^2=y^2+2y+1
->
(x-1)^2+(y+1)^2-2-1=0
(the -2 was added because both polynomials add +1)

(x-1)^2+(y+1)^2=3
this matches the form
(x-h)^2+(y+k)^2=r^2
->h=1
k=-1
r^2=3
r=sqrt(3)
so your center point is (h, k)=(1, -1) with the radius sqrt(3)

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