Reduce the equation to standard form, classify the surface and sketch it.

Question

Reduce the equation to standard form, classify the surface and sketch it.

x² = 2y² + 3z²

Answer 1

Obviously a flared 3-D hyperbolic tube of elliptical cross-section, centered at the origin. Obviously, since the variables are "separated" nicely! To sketch, just drop each of the variables in turn, and sketch the curve intersection with the respective "dropped" plane. Then just sketch a portion, cut strategically to display those intersection curves. At least, that's what I'd do; maybe you are more artistic?

-- Cheers, --Mr. d.