4x^2+9y^2=36
x^2/9+y^2/4=1
设x=3cosa,y=2sina
x+y=3cosa+2sina=根号(9+4)sin(a+m),(其中tan(m)=3/2)
由于-1<=sin(a+m)<=1
故x+y的取值范围是[-根号13,根号13]