Know your Surfaces, Part 2

Geometry Level 5

x 2 + 3 y 2 + 4 x y + 2 y z + 2 x z = 1 \large x^2+3y^2+4xy+2yz+2xz=1

What kind of surface is this?

Part 1 .

Elliptic Cylinder Ellipsoid Cone Hyperbolic Cylinder Hyperboloid of two Sheets Hyperboloid of one Sheet

Otto Bretscher by Otto Bretscher , 65, USA

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1 solution

Otto Bretscher
Mar 7, 2016

As we discussed here , it suffices to complete the squares, ( x + 2 y + z ) 2 − ( y + z ) 2 = 1 (x+2y+z)^2-(y+z)^2=1 . Since the coefficients are positive, negative and zero, this is a hyperbolic cylinder .

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