Let’s cut a sphere by a variable plane parallel to the base plane at a distance h from the center of the sphere. The section of the sphere by the plane is a circle of radius r.

Let’s represent the variations of r in function of h, in the system of axes (represented in the horizontal plane).

What is the graph of the function r(h) ? Justify the answer.

Hint : move the point H and observe the trajectory of the point of coordinates (h, r) in the axes.