HomeTextbook AnswersMathCalculusCalculus (3rd Edition)Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 63654
Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Chapter 17 Chapter 18 Appendix A Appendix C Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Preliminary Questions Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Preliminary Questions Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Preliminary Questions Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.3 Polar Coordinates - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Preliminary Questions Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.4 Area and Arc Length in Polar - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Preliminary Questions Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises Parametric Equations, Polar Coordinates, and Conic Sections - Chapter Review Exercises Parametric Equations, Polar Coordinates, and Conic Sections - Chapter Review Exercises 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.5 Conic Sections - Exercises - Page 636: 54
$$ r= -\frac{12}{2+ 3\cos \theta}. $$
The polar equation of the conic of eccentricity $e \gt0$, with focus at the origin and directrix $x = d$ is $$ r=\frac{e d}{1+e \cos \theta}. $$ Now, since $e=3/2$ and $x=-4$, then the polar equation is $$ r=\frac{-6}{1+ (3/2)\cos \theta} =-\frac{12}{2+ 3\cos \theta}. $$
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