Sample

Test 1

problem 1

problem 2

Test 2

problem 1

problem 2

3D graphs of the function
 (x^2)+a (y^2)

The case a>0

a = 1; 
    Plot3D[x^2 + a y^2, {x, -2, 2}, {y, -2, 2}, 
      PlotPoints -> 50]

The case a=0

a = 0; 
    Plot3D[x^2 + a y^2, {x, -2, 2}, {y, -2, 2}, 
      PlotPoints -> 50]

The case a<0

a = -1; 
    Plot3D[x^2 + a y^2, {x, -2, 2}, {y, -2, 2}, 
      PlotPoints -> 50]