33. 2 ²² = ( ² ) ² + ( ² ) ² 4 8
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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Just do 33 with explanation pleaseee!!!!
Transcribed Image Text:In Exercises 29–42, sketch the given surface.
29. \( x^2 + y^2 - z^2 = 1 \)
![**Equation 33:**
\[ z^2 = \left(\frac{x}{4}\right)^2 + \left(\frac{y}{8}\right)^2 \]
**Explanation:**
This equation represents a three-dimensional surface, specifically an elliptical cone. The equation is in standard form, indicating that the surface expands along the z-axis and has elliptical cross-sections with semi-axes proportional to 4 and 8 along the x and y directions respectively. To better understand this equation's geometric implications, one can analyze the scales of the x and y components, which dictate the shape and orientation of the elliptical sections.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec99e2ce-f146-4dfd-8358-2828b726596b%2F06b88b37-a3b3-4c47-8645-5d451eb1dc35%2Fjjkylbu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Equation 33:**
\[ z^2 = \left(\frac{x}{4}\right)^2 + \left(\frac{y}{8}\right)^2 \]
**Explanation:**
This equation represents a three-dimensional surface, specifically an elliptical cone. The equation is in standard form, indicating that the surface expands along the z-axis and has elliptical cross-sections with semi-axes proportional to 4 and 8 along the x and y directions respectively. To better understand this equation's geometric implications, one can analyze the scales of the x and y components, which dictate the shape and orientation of the elliptical sections.
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