The parametric equations of a line l parallel to v

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Unformatted text preview: ic paraboloid Matches graph (d) 9. y2 z2 9 Plane parallel to the xy-coordinate plane 2 3 x 2 The x-coordinate is missing so we have a cylindrical surface with rulings parallel to the x-axis. The generating curve is a circle. z 2 y 4 x 76 4 y 11. y x2 13. 4x2 x2 1 y2 y2 4 4 1 The z-coordinate is missing so we have a cylindrical surface with rulings parallel to the z-axis. The generating curve is a parabola. z 4 The z-coordinate is missing so we have a cylindrical surface with rulings parallel to the z-axis. The generating curve is an ellipse. z 3 x 4 3 2 3 4 y −3 2 3 x 2 3 y 250 15. z Chapter 10 sin y Vectors and the Geometry of Space z 2 1 y The x-coordinate is missing so we have a cylindrical surface with rulings parallel to the x-axis. The generating curve is the sine curve. 4 x 3 3 17. x x2 y2 (a) You are viewing the paraboloid from the x-axis: 20, 0, 0 (b) You are viewing the paraboloid from above, but not on the z-axis: 10, 10, 20 (c) You are viewing the paraboloid from the z-axis: 0, 0, 20 (d) You are viewing the paraboloid from the y-axis: 0, 20, 0 x2 1 y2 4 z2 1 2 19. 1 2 z 21. 16x 2 4x 2 y2 y2 4 16z 2 4z 2 1 4 3 2 z Ellipsoid x xy-trace: 1 y2 4 z2 z2 1 1 ellipse 2 −2 −3 Hyperboloid on one sheet x −2 2 y xz-trace: x 2 yz-trace: y2 4 1 circle 1 ellipse xy-trace: 4x 2 xz-trace: 4 x 2 yz-trace: y2 4 y2 4 z2 4z 2 2 1 hyperbola 1 circle 1 hyperbola 3 x −2 −3 3 y 23. x2 y z2 0 x2 z2 z2 z2 1 0, 25. x2 y2 z 0 ±x 27. z 2 x2 y2 4 Elliptic paraboloid xy-trace: y xz-trace: x2 yz-trace: y y 1: x2 z 3 2 1 2 1 3 −2 −3 4 y −3 Hyperbolic paraboloid xy-trace: y xz-trace: z yz-trace: z y ± 1: z z 3 Elliptic Cone xy-trace: point 0, 0, 0 xz-trace: z ±x ±1 x2 y2 1 x2 point 0, 0, 0 yz-trace: z z ± 1: x2 z 2 y2 4 y 1 x 32 23 y 2 1 −2 x 2 −2 2 y 3 x 29. 16x2 16 x2 2x 9y2 1 16 x 16z2 9 y2 1 x 1 2 32x 4y 9y 36y 4 2 2 2 36 16z2 16z2 z2 1 0 36 16 2 z 16 36 1 x 2 1 1 2 y2 16 9 2 −2 4 y 1 Ellipsoid with center 1, 2, 0 . Section 10.6 31. z 2 sin x z Surfaces in Space y2 ± 251 33. z 2 z x2 ± 4y 2 x2 z 35. x2 y 4y2 2...
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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