Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 45.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 673 Use the discriminant to decide whether the equation represents a parabola, an ellipse, or a hyperbola. 49.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page Find the center, vertices, and foci of the hyperbola in the original coordinate system.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page Find the center, vertices, and foci of the hyperbola in the original coordinate system.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page True, because there is no xy term to cause a rotation.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page A. (1±4, –2) B. (1±3, –2) C. (4±1, 3) D. (4±2, 3) E. (1, –2±3)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.5 Polar Equations of Conics
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 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.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 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.)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Focus-Directrix Eccentricity Relationship
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide A Conic Section in the Polar Plane
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Three Types of Conics for r = ke/(1+ecosθ)
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Identifying Conics from Their Polar Equations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Matching Graphs of Conics with Their Polar Equations
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding Polar Equations of Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding Polar Equations of Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework #23 Review Section 8.5 Page 682, Exercises: 1 – 29(EOO) Quiz next time
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Semimajor Axes and Eccentricities of the Planets
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Ellipse with Eccentricity e and Semimajor Axis a