Answer
The interior of the circle of radius $r=\sqrt{3}$, centered at the origin, including the circle itself.
Work Step by Step
Equation (1) in the text,
$(x-h)^{2}+(y-k)^{2}=r^{2}$
is the standard equation for a circle of radius $r,$ centered at $(h,k)$,
$x^{2}+y^{2}=3$
is a circle of radius $r=\sqrt{3}$, centered at the origin.
This circle divides the plane into two regions: the interior and exterior of the circle.
Testing coordinates of the origin,
$0^{2}+0^{2}\leq 3,$
we see that the origin belongs to the solution set.
The inequality sign $\leq$ indicates that the border line (the circle) is included in the solution set.
The region represented by the inequality is the interior of the circle of radius $r=\sqrt{3}$, centered at the origin, including the circle itself.
