representing the arc length of the curve C.2. Consider the equation x2 + y? = 8x + z – 4.%3D(a) Convert this equation into one involving cylindrical coordinates.(b) Convert this equation into one involving spherical coordinates.(c) Determine the coordinates of one point P on this surface and express this point usingrectangular, cylindrical, and spherical coordinates.

Answered: representing the arc length of the…

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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representing the arc length of the curve C.
2. Consider the equation x2 + y? = 8x + z – 4.
%3D
(a) Convert this equation into one involving cylindrical coordinates.
(b) Convert this equation into one involving spherical coordinates.
(c) Determine the coordinates of one point P on this surface and express this point using
rectangular, cylindrical, and spherical coordinates.

Expert Solution

Step 1

$G i v e n : x^{2} + y^{2} = 8 x + z - 4 (a) T o c o n v e r t f r o m r e c \tan g u l a r t o c y l i n d r i c a l c o o r d i n a t e s w e u s e r^{2} = x^{2} + y^{2} \tan θ = \frac{y}{x} z = z A n d w e k n o w x = r \cos θ y = r \sin θ C o n s i d e r x^{2} + y^{2} = 8 x + z - 4 S u b s t i t u t e f o r x a n d y w e g e t r^{2} = 8 r \cos θ + z - 4 E q u a t i o n i n c y l i n d r i c a l c o o r d i n a t e s i s r^{2} - 8 r \cos θ - z + 4 = 0$

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