Findanhe surfore atthetoan equation of the homaent planesiven hoind,6292(-7-70

Answered: Findan he surfore atthe to an equation…

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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Question

Findan
he surfore atthe
to
an equation of the homaent plane
siven hoind,
62
92
(-7-70

Expert Solution

Step 1

Consider the given equation $F (x, y, z) = x^{2} + y^{2} - 6 z^{2} - 92 = 0$ and the points $(x_{0}, y_{0}, z_{0}) = (- 7, - 7, 1)$ .

That implies,

$F_{x} (x, y, z) = 2 x F_{x} (- 7, - 7, 1) = 2 (- 7) = - 14 F_{y} (x, y, z) = 2 y F_{y} (- 7, - 7, 1) = 2 (- 7) = - 14 F_{z} (x, y, z) = - 12 z F_{z} (- 7, - 7, 1) = - 12 (1) = - 12$

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