Prove that at (x, y, z) the point of intersection of three confocals t² 1,² z² 2+₁b²+² c²+1 + + ,2 -Ł.² + = z² and + + + µ 6² +μ c²² +μ the osculating plane of the curve of intersection of the first two is given by xx₁₂(a² + \ a² (a² + 2) Σ = + = 1 = 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 27E
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and
Prove that at (x, y, z₁) the point of intersection of three confocals
z²
ܐܐ ܐ
+ + = 1
6²
c.²
4.²
z²
+
+
2
a² +μ b²+ (²²
ܕܐ
+μ
Σ
= 1,
AAA
+
+
a² + λ b² +^
c² + λ
the osculating plane of the curve of intersection of the first two is given by
xx₁ (a² +
a²
μ)
(a² + 2)
=1
= 1
Transcribed Image Text:and Prove that at (x, y, z₁) the point of intersection of three confocals z² ܐܐ ܐ + + = 1 6² c.² 4.² z² + + 2 a² +μ b²+ (²² ܕܐ +μ Σ = 1, AAA + + a² + λ b² +^ c² + λ the osculating plane of the curve of intersection of the first two is given by xx₁ (a² + a² μ) (a² + 2) =1 = 1
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