Answer
The ring (or washer) containing points between two concentric circles about the origin, with radii 1 and 2. The circles are excluded from the solution set.
(The set of points at a distance of more than 1 but less than 2 units from the origin).
Work Step by Step
$x^{2}+y^{2} \gt 1$
Is the exterior of the circle $\quad x^{2}+y^{2} = 1$,
which is centered at the origin and has radius 1.
$x^{2}+y^{2} \lt 4$
Is the interior of the circle $\quad x^{2}+y^{2} = 2^{2}$,
which is centered at the origin and has radius $2$.
Neither region includes its border curve (the circle), because the inequalities are strict.
The solution set is:
The ring (or washer) containing points between two concentric circles about the origin, with radii 1 and 2. The circles are excluded from the solution set.
(The set of points at a distance of more than 1 but less than 2 units from the origin).
