x2+2z2=y
Let's rewrite equation: 2x2+4z2=2y⟺0.5x2+0.25z2=2y
Now we can see that our surface is elliptic paraboloid.
Denominators are unequal. It means that our paraboloid is not a paraboloid of revolution.
Let x=0, then y=2z2
And let z=0, then y=x2
y=2z2 and y=x2 principal parabolas.
Let's look on sections.
y=c, where c∈R
x2+2y2=c− ellipses if c>0
If x=c, where c∈R
y=2z2+c2− parabolas.
c2− is distance between the origin and vertex of parabola.
A similar result will be if we look at z=c, where c∈R
y=x2+2c2
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