718 Chapter 12: Vectors and the Geometry of Space Exercises 12.6 Matching Equati

Question

718 Chapter 12: Vectors and the Geometry of Space Exercises 12.6 Matching Equations with surfaces In Exercises 1-12, match the equation with the surface it defines. Also, identify each surface by type (paraboloid, ellipsoid, etc.) The surfaces are labeled (a)(1). 10 2. 22 + 4y 10. z Drawing Sketch the surfaces in Exercises 13–44. 11 + 42 12. 9x + 4yº+ 22 = 36 CYLINDERS 13. x2 + y? = 4 15. x2 + 4z = 16 14. 2 = y 16. 4x2 + y = 36 ELLIPSOIDS 17.9x2+ y2 + 2 = 9 18. 4x2 + 4y + 2 = 16 19. 4x + 9y? + 42 = 36 20.9x + 4y? + 36; 2 = 36 PARABOLOIDS AND CONES 21. z x + 4y 22. z 23. x 25. x2 + y 24. y 26+ 922 = 9.2 . 4x HYPERBOLOIDS 27. x2 + y 29. . 28. y2 + 2 - 2 = 1 30. (v2/4) - (/4 ) - - 1 HYPERBOLIC PARABOLOIDS 31. y 32. X ASSORTED 33. 2 35. y (x2 +2) 34. 4x + 4yº = 36. 16x2 + 4y = 1 37. x + y" 38. X + 39. x 40. 16y + 9.2 = 4x2 41. z (x2 + y?) 43. 4y + 22 - 4x2 = 4 42. 44. x + y" Theory and examples 45. . Express the area A of the cross-section cut from the ellipsoid by the plane z c as a function of c. (The area of an ellipse with semiaxes a and b is Tab.) b. Use slices perpendicular to the 3-axis to find the volume of the ellipsoid in part (a). C. Now find the volume of the ellipsoid Does your formula give the volume of a sphere of radius a if

Explanation / Answer

1 matches to d

2 matches to j

3 matches to b

4 matches to h

5 matches to k

6 matches to e

7 matches to a

8 matches to i

9 matches to l

10 matches to f

11 matches to g

12 matches to c

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