Let us graph the circle x^2+y^2=36, which is a circle with center (0,0) and radius 6 and x^2+y^2<36 is the set of all points lying inside the circle but not on the circle, as we have inequality. It would have included points on the circle had the inequality been x^2+y^2<=36. The graph of x^2+y^2<36, appears as follows:
graph{x^2+y^2<36 [-14, 14, -7, 7]}
Similarly, 4x^2+9y^2>36 is the graph is the set of all points lying outside the ellipse but not on the circle. Its graph appears as follows:
graph{4x^2+9y^2>36 [-14, 14, -7, 7]}
And solution of the system of inequalities x^2+y^2=36 and 4x^2+9y^2>36 is the set of intersection of points in the two.
Thus it includes points outside the ellipse 4x^2+9y^2=36 but inside the circle x^2+y^2=36 but does not include points on the circle and the ellipse. The region appears as shown below.
![enter image source here]()
