Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 673 Solve for y and use a function grapher to graph the conic. 9.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 673 Write an equation in standard form for the conic shown. 13.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 673 Using the point P(x, y) and the translation information given, find coordinates of P in the translated x’y’ coordinate system.. 17.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 21.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 25.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 673 Identify the type of conic, write the equation in the standard form, translate the conic to the origin, and sketch it in the translated coordinate system. 29.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 What you’ll learn about Rotation of Axes Discriminant Test … and why You will see ellipses, hyperbolas, and parabolas as members of the family of conic sections rather than as separate types of curves.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Rotation of Cartesian Coordinate Axes
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Rotation of Cartesian Coordinate Axes
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Rotation-of-Axes Formulas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Rotation of Axes
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Coefficients for a Conic in a Rotated System
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Angle of Rotation to Eliminate the Cross- Product Term
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Discriminant Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Using Discriminant Test
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Conics and the Equation Ax 2 +Bxy+Cy 2 +Dx+Ey+F=0
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework Assignment #21 Read Section 8.5 Page 673, Exercises: 33 – 61(EOO)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.5 Polar Equations of Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Quick Review
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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 The Geometric Structure of a Conic Section
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)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Polar Equations for Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Writing Polar Equations of Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Writing Polar Equations of Conics
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 Identifying Conics from Their Polar Equations
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