MediumConic sections

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §3.5 Parabolas, Ellipses, and Hyperbolas, #26 · Geometry · Conic sections

A tilted cylinder has equation surface

This problem is about parabolas, are about ellipses, are about hyperbolas.

A tilted cylinder has equation surface $(x - 2 y - 2 z)^{2} + (y - 2 x - 2 z)^{2} = 1$ . Show that the water surface at $z = 0$ is an ellipse. What is its equation and what is $B^{2} - 4 A C$ ?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §3.5 Parabolas, Ellipses, and Hyperbolas, #26

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