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prove hat for 4 x² + y² + z² + 6xyz + 2x² - y² +z²+ 4yz + 3zx = 0, rigin is a conic node. the locus of the tangents at the origin is the cone 2x² - y² +z²+4yz + 3zx = 0 The six tangents which have four point contact are

prove hat for 4 x² + y² + z² + 6xyz + 2x² - y² +z²+ 4yz + 3zx = 0, rigin is a conic node. the locus of the tangents at the origin is the cone 2x² - y² +z²+4yz + 3zx = 0 The six tangents which have four point contact are

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Q. prove that for the surface x² + y² + z² + 6xyz + 2x² - y² + z² + 4yz + 3zx = 0, the origin is a conic node. the locus of the tangents at the origin is the cone 2x² - y² + z² + 4yz + 3zx = 0 The six tangents which have four point contact are I x = 0, y = (2+ √5)z; y = 0, 2x +z = 0; y = 0, x + z = 0; z = 0, V2x = ±y.
Transcribed Image Text:Q. prove that for the surface x² + y² + z² + 6xyz + 2x² - y² + z² + 4yz + 3zx = 0, the origin is a conic node. the locus of the tangents at the origin is the cone 2x² - y² + z² + 4yz + 3zx = 0 The six tangents which have four point contact are I x = 0, y = (2+ √5)z; y = 0, 2x +z = 0; y = 0, x + z = 0; z = 0, V2x = ±y.
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