Consider the following equation of a quadric surface. x² 2 2 y² z² 441 441 441=1 a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Sketch a graph of the surface.

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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### Consider the following equation of a quadric surface:

\[
\frac{x^2}{441} + \frac{y^2}{441} - \frac{z^2}{441} = 1
\]

a. Find the intercepts with the three coordinate axes, if they exist.

b. Find the equations of the xy-, xz-, and yz-traces, if they exist.

c. Sketch a graph of the surface.

---

### Task:

a. Find the x-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- **A. The x-intercept(s) is/are located at \(x = \) [ ]**  
  *(Use a comma to separate answers as needed.)*

- **B. There are no x-intercepts.**
Transcribed Image Text:### Consider the following equation of a quadric surface: \[ \frac{x^2}{441} + \frac{y^2}{441} - \frac{z^2}{441} = 1 \] a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Sketch a graph of the surface. --- ### Task: a. Find the x-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - **A. The x-intercept(s) is/are located at \(x = \) [ ]** *(Use a comma to separate answers as needed.)* - **B. There are no x-intercepts.**
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x squared over 441 plus y squared over 441 minus z squared over 441 equals 1

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