is an elliptic paraboloid
centered on the positive y-axis.
with its graph (labeled I-VIII). Give reasons for your choice.
Solution: The surface
is an elliptic paraboloid
centered on the positive y-axis.
The reasons:
For fixed y > 0 the equation 
is the equation of an ellipse.
Setting z = 0 we have the parabola
Setting x = 0 we have the parabola 
.
The only possible solution is the graph VI.
by: gm