Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question

19

10. (a) Find and identify the traces of the quadric surface -x² - y² + z² = 1 and explain why the graph looks like the graph of the hyperboloid of two sheets in Table 1. (b) If the equation in part (a) is changed to x² - y² - z² = 1, what happens to the graph? Sketch the new graph. 1 11-20 Use traces to sketch and identify the surface. 11. x = y² + 4z² 12. 4x² +9y² + 9z² = 36 13. x² = 4y² + z² 14. z² - 4x² - y² = 4 15. 9y² + 4z² = x² + 36 1 16. 3x² + y + 3z² = 0 llohen os x² bam z² + + = 1 plochany 18. 3x² - y² + 3z² = 0 9 25 4 di sis minog od 17. 19. y = z² - x² I y2 21-28 Match the equation with its graph (labeled I-VIII). Give reasons for your choice. 21. x² + 4y² + 9z² = 1 23. x² - y² + z² = 1 25. y = 2x² + z² 2 27. x² + 2z² = 1 III X Z Z 20. x = y² = z² II 22. 9x² + 4y² + z² = 1 24. -x² + y² - z² = 1 26. y² = x² + 2z² 28. y = x² - z² IV XX ZA ZA y 29-3 trace 29. 30. 31 th 3 3:
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Transcribed Image Text:10. (a) Find and identify the traces of the quadric surface -x² - y² + z² = 1 and explain why the graph looks like the graph of the hyperboloid of two sheets in Table 1. (b) If the equation in part (a) is changed to x² - y² - z² = 1, what happens to the graph? Sketch the new graph. 1 11-20 Use traces to sketch and identify the surface. 11. x = y² + 4z² 12. 4x² +9y² + 9z² = 36 13. x² = 4y² + z² 14. z² - 4x² - y² = 4 15. 9y² + 4z² = x² + 36 1 16. 3x² + y + 3z² = 0 llohen os x² bam z² + + = 1 plochany 18. 3x² - y² + 3z² = 0 9 25 4 di sis minog od 17. 19. y = z² - x² I y2 21-28 Match the equation with its graph (labeled I-VIII). Give reasons for your choice. 21. x² + 4y² + 9z² = 1 23. x² - y² + z² = 1 25. y = 2x² + z² 2 27. x² + 2z² = 1 III X Z Z 20. x = y² = z² II 22. 9x² + 4y² + z² = 1 24. -x² + y² - z² = 1 26. y² = x² + 2z² 28. y = x² - z² IV XX ZA ZA y 29-3 trace 29. 30. 31 th 3 3:
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