Question

x^2+y^2+2x-2y=-1

find vertex and radius

Answer 1

this is an equation of a circle

general form is (x-a)^2 + (y-b)^2 = r^2
where a,b is the centre and r = radius
using completeing the square will let you figure these values out

Answer 2

\[x^2+2x+y^2-2y=-1\] reorder
\[x^2+2x+(2/2)^2+y^2-2y+(-2/2)^2=-1+(2/2)^2+(-2/2)^2\] whatever you add to one side you add to the other
\[(x+1)^2+(y-1)^2=-1+1+1\]
\[(x+1)^2+(y-1)^2=1\]

Answer 3

center is (-1,1)
radius is 1