O15-C900
> restart;

> g:=(9-x^2-y^2)/4/(x^2+y^2+6*x+9);

                                       2    2
                                  9 - x  - y
                      g := 1/4 -----------------
                                2    2
                               x  + y  + 6 x + 9

> simplify(diff(g,x,x)+diff(g,y,y));

                                  0

> x:=r*cos(t):y:=r*sin(t):z:=subs({x=r*cos(t),y=r*sin(t)},g);

                              2       2    2       2
                         9 - r  cos(t)  - r  sin(t)
          z := 1/4 ----------------------------------------
                    2       2    2       2
                   r  cos(t)  + r  sin(t)  + 6 r cos(t) + 9

> simplify(subs(r=1,z));

                                  1
                             ------------
                             5 + 3 cos(t)

> plot3d([x,y,z],r=0..1,t=-Pi..Pi);

> 
>