Question

Identify the given surface x^2+4y^2-10z=0

Answer 1

level curves are
x=0 :
z= (2/5)*y^2 (parabola in the yz)

y=0 :
z= (1/10) *x^2 (parabola in the xz plane)

z=C
x^2 +4y^2 =10C (ellipses parallel to the xy plane)

so it's a...?