EDB — 1Q4

[1Q4]Let \(a{\gt}0\). Show that the equation \(\sqrt x + \sqrt y + \sqrt z = \sqrt a\) defines a regular surface inside the first octant \(\{ x{\gt}0,y{\gt}0,z{\gt}0\} \). Prove that planes tangent to the surface cut the three coordinate axes at three points, the sum of whose distances from the origin is constant.