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Homework, Page 673

Homework, Page 673. Using the point P ( x, y ) and the rotation information, find the coordinates of P in the rotated x’y’ coordinate system. 33. Homework, Page 673.

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Homework, Page 673

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  1. Homework, Page 673 Using the point P(x, y) and the rotation information, find the coordinates of P in the rotated x’y’ coordinate system. 33.

  2. Homework, Page 673 Identify the type of conic, and rotate the coordinate system to eliminate the xy-term. Write and graph the transformed equation. 37.

  3. Homework, Page 673 Identify the type of conic, solve for y, and graph the conic. Approximate the angle of rotation needed to eliminate the xy-term. 41.

  4. Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 45.

  5. Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 49.

  6. Homework, Page 673 53. Find the center, vertices, and foci of the hyperbola in the original coordinate system.

  7. Homework, Page 673 53. Find the center, vertices, and foci of the hyperbola in the original coordinate system.

  8. Homework, Page 673 57. True, because there is no xy term to cause a rotation.

  9. Homework, Page 673 61. A. (1±4, –2) B. (1±3, –2) C. (4±1, 3) D. (4±2, 3) E. (1, –2±3)

  10. 8.5 Polar Equations of Conics

  11. Quick Review

  12. Quick Review Solutions

  13. What you’ll learn about • Eccentricity Revisited • Writing Polar Equations for Conics • Analyzing Polar Equations of Conics • Orbits Revisited … and why You will learn the approach to conics used by astronomers.

  14. Focus-Directrix Definition Conic Section A conic section is the set of all points in a plane whose distances from a particular point (the focus) and a particular line (the directrix) in the plane have a constant ratio. (We assume that the focus does not lie on the directrix.)

  15. Focus-Directrix Eccentricity Relationship

  16. A Conic Section in the Polar Plane

  17. Three Types of Conics for r = ke/(1+ecosθ)

  18. Polar Equations for Conics

  19. Example Writing Polar Equations of Conics

  20. Example Identifying Conics from Their Polar Equations

  21. Example Matching Graphs of Conics with Their Polar Equations

  22. Example Finding Polar Equations of Conics

  23. Example Finding Polar Equations of Conics

  24. Homework • Homework #23 • Review Section 8.5 • Page 682, Exercises: 1 – 29(EOO) • Quiz next time

  25. Semimajor Axes and Eccentricities of the Planets

  26. Ellipse with Eccentricity e and Semimajor Axis a

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