Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 1 Homework, Page 653 Find the vertices and foci of the ellipse. 1.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 2 Homework, Page 653 Find the vertices and foci of the ellipse. 5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 3 Homework, Page 653 Match the graph to the equation given that all of the ticks represent one unit. 9. a.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 4 Homework, Page 653 Sketch the graph of the ellipse by hand. 13.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 5 Homework, Page 653 Graph the ellipse using a function grapher. 17.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 6 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 21.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 7 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 25.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 8 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 29.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8- 9 Homework, Page 653 Find an equation for the ellipse that satisfies the given conditions. 33.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 653 Find center, vertices, and foci of the ellipse. 37.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 653 Graph the ellipse using a parametric grapher. 41.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 653 Prove the graph of the equation is an ellipse, and find its vertices, foci, and eccentricity. 45.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 653 Write an equation for the ellipse. 49.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The Moon’s apogee is 252,710 mi, and perigee is 221,463 mi. Assuming the Moon’s orbit is elliptical, with the Earth at one focus, calculate and interpret a, b, c, and e.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The sun grazers pass within a Sun’s diameter of the solar surface. What can you conclude about a – c for orbits of sun grazers? (From problem #54, we know that the diameter of the Sun is about Gm.)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 653 Solve the system of equations algebraically and support your answer graphically. 61.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page The distance from a focus of an ellipse to the closer vertex is a(1 + e) where a is a semimajor axis and e is the eccentricity. Justify your answer
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page A. (4, 2) B. (4, 3) C. (4, 4) D. (4, 5) E. (4, 6)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.3 Hyperbolas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Geometry of a Hyperbola Translations of Hyperbolas Eccentricity and Orbits Reflective Property of a Hyperbola Long-Range Navigation … and why The hyperbola is the least known conic section, yet it is used in astronomy, optics, and navigation.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Hyperbola A hyperbola is the set of all points in a plane whose distances from two fixed points in the plane have a constant difference. The fixed points are the foci of the hyperbola. The line through the foci is the focal axis. The point on the focal axis midway between the foci is the center. The line through the center and perpendicular to the focal axis is the conjugate axis. The points where the hyperbola intersects its focal axis are the vertices of the hyperbola. The line collinear with the focal axis and connecting the vertices is the transverse axis.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Hyperbola
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Hyperbola
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding the Vertices and Foci of a Hyperbola
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Sketching a Hyperbola by Hand
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding an Equation of a Hyperbola
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Hyperbola with Center (h,k)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Hyperbola with Center (h,k)
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Locating Key Points of a Hyperbola
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Locating a Point Using Hyperbolas Radio signals are sent simultaneously from three transmitters located at O, Q, and R. R is 80 miles due north of O and Q is 100 miles due east of O. A ship receives the transmission from O μsec after the signal from R and μsec after the signal from Q. What is the ship’s bearing and distance from O?
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Locating a Point Using Hyperbolas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Eccentricity of a Hyperbola
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework Assignment #18 Review Section 8.3 Page 663, Exercises: 1 – 65(EOO), skip 53
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 8.4 Translations and Rotations of Axes
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about Second-Degree Equations in Two Variables Translating Axes versus Translating Graphs … 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 Example Plotting Conics
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Writing Conic Equations From Graphs
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Translation-of-Axes Formulas
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Translation of Cartesian Coordinate Axes
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Example Finding Coordinates of a Point in a Translated Coordinate System Using the point P (x, y) and the translation information, find the coordinates of P in the translated x’y’ coordinate system. 20.
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