Answers: C and D
Step-by-step explanation
The function f(x,y) plots out a 3D surface. The shape is a bowl.
The level curves are cross sectional pieces of the surface. They result when we intersect a flat plane with the surface. On maps level curves are known as contour lines. They are curves in which the elevation is the same throughout the curve.
What we do is refer to the form f(x,y) = k where k is constant.
If k = 1 for instance, then we arrive at x^2+y^2 = 1 which is the unit circle.
When k = 4, we have:
x^2+y^2 = 4
0 = 4-x^2-y^2
4 - x^2 - y^2 = 0
This is a circle of radius 2.
The value of k describes our elevation on the z axis. For instance k = 0 describes the ground level, k = 1 can be thought of as the 1st floor, k = 2 is the 2nd floor, and so on.
Note how as k increases, the radius increases. This matches with the fact the 3D bowl shape gets wider as you increase the elevation.