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9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere centered at (a,0,0) with radius |a]. %3D

9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere centered at (a,0,0) with radius |a]. %3D

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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Please answer question 9 on the screenshot in the post. Please give a full explanation to each of the steps. 

**Exercises** **A** For Exercises 1-4, find the (a) cylindrical and (b) spherical coordinates of the point whose Cartesian coordinates are given. 1. \( (2, 2\sqrt{3}, -1) \) 2. \( (-5, 5, 6) \) 3. \( (\sqrt{21}, -\sqrt{7}, 0) \) 4. \( (0, \sqrt{2}, 2) \) For Exercises 5-7, write the given equation in (a) cylindrical and (b) spherical coordinates. 5. \( x^2 + y^2 + z^2 = 25 \) 6. \( x^2 + y^2 = 2y \) 7. \( x^2 + y^2 + 9z^2 = 36 \) **B** 8. Describe the intersection of the surfaces whose equations in spherical coordinates are \( \theta = \frac{\pi}{2} \) and \( \phi = \frac{\pi}{4} \). 9. Show that for \( a \neq 0 \), the equation \( \rho = 2a \sin \phi \cos \theta \) in spherical coordinates describes a sphere centered at \( (a, 0, 0) \) with radius \( |a| \).
Transcribed Image Text:**Exercises** **A** For Exercises 1-4, find the (a) cylindrical and (b) spherical coordinates of the point whose Cartesian coordinates are given. 1. \( (2, 2\sqrt{3}, -1) \) 2. \( (-5, 5, 6) \) 3. \( (\sqrt{21}, -\sqrt{7}, 0) \) 4. \( (0, \sqrt{2}, 2) \) For Exercises 5-7, write the given equation in (a) cylindrical and (b) spherical coordinates. 5. \( x^2 + y^2 + z^2 = 25 \) 6. \( x^2 + y^2 = 2y \) 7. \( x^2 + y^2 + 9z^2 = 36 \) **B** 8. Describe the intersection of the surfaces whose equations in spherical coordinates are \( \theta = \frac{\pi}{2} \) and \( \phi = \frac{\pi}{4} \). 9. Show that for \( a \neq 0 \), the equation \( \rho = 2a \sin \phi \cos \theta \) in spherical coordinates describes a sphere centered at \( (a, 0, 0) \) with radius \( |a| \).
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