EVEN09 - CHAPTER 9 Conics Parametric Equations and Polar...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
C H A P T E R 9 Conics, Parametric Equations, and Polar Coordinates Section 9.1 Conics and Calculus . . . . . . . . . . . . . . . . . . . . 424 Section 9.2 Plane Curves and Parametric Equations . . . . . . . . . . 434 Section 9.3 Parametric Equations and Calculus . . . . . . . . . . . . 439 Section 9.4 Polar Coordinates and Polar Graphs . . . . . . . . . . . . 444 Section 9.5 Area and Arc Length in Polar Coordinates . . . . . . . . . 452 Section 9.6 Polar Equations of Conics and Kepler’s Laws . . . . . . . 458 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
C H A P T E R 9 Conics, Parametric Equations, and Polar Coordinates Section 9.1 Conics and Calculus Solutions to Even-Numbered Exercises 424 2. Vertex: Opens upward Matches graph (a). p 2 > 0 0, 0 x 2 8 y 4. Center: Ellipse Matches (b) 2, 1 x 2 2 16 y 1 2 4 1 6. Circle radius 3. Matches (g) x 2 9 y 2 9 1 8. Hyperbola Center: Horizontal transverse axis. Matches (d) 2, 0 x 2 2 9 y 2 4 1 10. Vertex: Focus: Directrix: y 2 0, 2 0, 0 x 4 8 4 8 4 8 12 (0, 0) y x 2 4 2 y x 2 8 y 0 12. Vertex: Focus: Directrix: y 0 1, 4 x 4 8 4 8 4 8 12 (1, 2) y 1, 2 x 1 2 4 2 y 2 x 1 2 8 y 2 0 14. Vertex: Focus: Directrix: x 0 4, 3 x 4 8 4 8 12 16 20 8 12 ( 2, 3) y 2, 3 y 3 2 4 2 x 2 y 2 6 y 9 8 x 25 9 y 2 6 y 8 x 25 0 16. Vertex: Focus: Directrix: x 4 0, 2 x 4 4 2 6 4 6 2 8 6 4 (2, 2) y 2, 2 y 2 2 4 2 x 2 y 2 4 y 4 8 x 12 4 y 2 4 y 8 x 12 0
Image of page 2
Section 9.1 Conics and Calculus 425 18. Vertex: Focus: Directrix: y 19 6 4, 1 6 2 4 10 4 4, 5 3 x 4 2 4 3 2 y 5 3 x 4 2 6 y 5 3 6 y 10 x 4 2 6 y x 4 2 10 y 1 6 x 2 8 x 6 1 6 x 2 8 x 16 10 20. Vertex: Focus: Directrix: y 1 1, 3 10 10 8 2 1, 1 x 1 2 4 2 y 1 x 2 2 x 1 8 y 9 1 x 2 2 x 8 y 9 0 22. x 2 2 x 8 y 15 0 x 1 2 4 2 y 2 24. Vertex: y 2 8 x 4 y 4 0 y 2 2 4 2 x 0 0, 2 26. x 2 4 x y 0 y 4 x 2 2 4 x x 2 28. From Example 2: or Vertex: x 2 8 x 8 y 16 0 x 4 2 8 y 0 4, 0 p 2 4 p 8 30. , Center: Foci: Vertices: e 2 14 14 7 ± 14 , 0 ± 2, 0 0, 0 c 2 4 b 2 10 a 2 14, x 2 14 y 2 10 1 x 2 2 4 4 6 6 6 2 6 4 y 5 x 2 7 y 2 70 32. Center: Foci: Vertices: e 3 2 1, 4 , 3, 4 2 ± 3 2 , 4 2, 4 c 2 3 4 b 2 1 4 , a 2 1, x 1 2 3 4 5 5 4 3 2 1 ( 2, 4) y x 2 2 1 y 4 2 1 4 1 34. Center: Foci: Vertices: e c a 3 5 2 ± 10 4 , 3 2 ± 3 10 20 , 3 2, 3 a 2 , 5 8 , b 2 2 5 , c 2 a 2 b 2 9 40 x 2 2 5 8 y 3 2 2 5 1 (2, 3) 1 1 2 3 4 1 1 2 3 4 y x 10 16 x 2 4 x 4 25 y 2 6 y 0 279 64 225 16 x 2 25 y 2 64 x 150 y 279 0
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
36. Center: Foci: Vertices: Solve for y : (Graph each of these separately.) y 2 ± 1 3 36 x 2 48 x 7 y 2 2 36 x 2 48 x 7 9 9 y 2 4 y 4 36 x 2 48 x 43 36 1 2 4 3 2 3 , 3 , 2 3 , 1 2 3 , 2 ± 3 2 2 3 , 2 c 2 3 4 b 2 1 4 , a 2 1, x 2 3 2 1 4 y 2 2 1 1 9 36 x 2 4 3 x 4 9 9 y 2 4 y 4 43 16 36 36 x 2 9 y 2 48 x 36 y 43 0 426 Chapter 9 Conics, Parametric Equations, and Polar Coordinates 38. Center: Foci: Vertices: Solve for y : (Graph each of these separately.) y 3.2 ± 7.12 4 x 2 x 2 y 3.2 2 7.12 4 x 2 x 2 y 2 6.4 y 10.24 2 x 2 4.8 x 3.12 10.24 6 5 , 16 5 ± 10 1 5 7 7 6 5 , 16 5 ± 5 6 5 , 16 5 a 2 10, b 2 5, c 2 5 x 6 5 2 5 y 16 5 2 10 1 50 x 2 12 5 x 36 25 25 y 2 32 5 y 256 25 78 72 256 250 50 x 2 25 y 2 120 x 160 y 78 0 2 x 2 y 2 4.8 x 6.4 y 3.12 0 40. Vertices: Eccentricity: Horizontal major axis Center: x 2 2 4 y 2 2 3 1 c 1 b 3 a 2, 2, 2 1 2 0, 2 , 4, 2 42 Foci: Major axis length: 14 Vertical major axis
Image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern