Consider x² 441 the following equation of a quadric surface. y² z² 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. 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 = -21,21. (Use a comma to separate answers as needed.) OB. There are no x-intercepts. C Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is/are located at y = 21, -21. (Use a comma to separate answers as needed.) OB. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The z-intercept(s) is/are located at z = (Use a comma to separate answers as needed.) B. There are no z-intercepts. b. Find the equation of the xy-trace, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The trace is not a single point. The equation of the xy-trace is OB. The trace is a single point (... O c. There is no xy-trace.
Consider x² 441 the following equation of a quadric surface. y² z² 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. 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 = -21,21. (Use a comma to separate answers as needed.) OB. There are no x-intercepts. C Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is/are located at y = 21, -21. (Use a comma to separate answers as needed.) OB. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The z-intercept(s) is/are located at z = (Use a comma to separate answers as needed.) B. There are no z-intercepts. b. Find the equation of the xy-trace, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. The trace is not a single point. The equation of the xy-trace is OB. The trace is a single point (... O c. There is no xy-trace.
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
![**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.
---
**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 \( x = -21, 21 \).
(Use a comma to separate answers as needed.)
- B. There are no x-intercepts.
**Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- (✓) A. The y-intercept(s) is/are located at \( y = 21, -21 \).
(Use a comma to separate answers as needed.)
- B. There are no y-intercepts.
**Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- A. The z-intercept(s) is/are located at \( z = \).
(Use a comma to separate answers as needed.)
- (✓) B. There are no z-intercepts.
---
**b. Find the equation of the xy-trace, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- A. The trace is not a single point. The equation of the xy-trace is \( \).
- B. The trace is a single point \( \left( , \right) \).
- C. There is no xy-trace.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ade5d6c-ff37-4df2-b1de-522b52697cc9%2F86ec7bd9-b724-41a0-a7fc-649318d7a187%2F7mfiiin_processed.png&w=3840&q=75)
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.
---
**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 \( x = -21, 21 \).
(Use a comma to separate answers as needed.)
- B. There are no x-intercepts.
**Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- (✓) A. The y-intercept(s) is/are located at \( y = 21, -21 \).
(Use a comma to separate answers as needed.)
- B. There are no y-intercepts.
**Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- A. The z-intercept(s) is/are located at \( z = \).
(Use a comma to separate answers as needed.)
- (✓) B. There are no z-intercepts.
---
**b. Find the equation of the xy-trace, if it exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.**
- A. The trace is not a single point. The equation of the xy-trace is \( \).
- B. The trace is a single point \( \left( , \right) \).
- C. There is no xy-trace.
Expert Solution
Step 1: To find.
In this question, we will find the intercept equation of traces and graph of the function.
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