Answer
Center: $(0,0)$
Radius: $r=1$
Work Step by Step
The equation of a circle in standard form:
$(x-h)^2+(y-k)^2=r^2$ in which $(h,k)$ is the center and $r$ is the radius
$x^2+y^2=1$
$(x-0)^2+(y-0)^2=1^2$
Center: $(0,0)$
Radius: $r=1$