Explanation Definition used: “The polar equation of a conic with focus at the origin and the directrix x = d is r = e d 1 + e cos θ .” Note 1: “The conics r = e d 1 ± e sin θ and r = e d 1 ± e cos θ represents, (i) An ellipse if 0 < e < 1 . (ii) A parabola if e = 1 . (iii) A hyperbola if e > 1 .” Formulae used: cos 0 = 1 , cos π 2 = 0 , cos π = − 1 , cos 3 π 2 = 0 . Calculation: Given the polar equation of conic is r = 6 1 + cos θ (1) Compare the equation (1) with r = e d 1 + e cos θ . By definition, it is observed that, e = 1 and d = 6 . That is, equation (1) is a parabola opens leftwards. From the set graphs it is observed that the graph II is the only parabola opens leftward. To conclude that the equation (1) matches graph II, find the intersection of the graph on the lines θ = 0 , θ = π 2 , θ = π and θ = 3 π 2 as follows. When θ = 0 , the value of r is computed as follows. r = 6 1 + cos 0 = 6 2 = 3 When θ = π 2 , the value of r is computed as follows. r = 6 1 + cos π 2 = 6 1 + 0 = 6 When θ = π , the value of r is computed as follows

Precalculus - Mathematics for Calculus - Seventh Edition

7th Edition

ISBN: 9781305750463

Author: Stewart

Publisher: CENGAGE C

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Chapter 11.6, Problem 11E

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To match: The polar equation r=61+cosθ with the graphs labeled I to VI.

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Chapter 11.6, Problem 10E

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Chapter 11 Solutions

Precalculus - Mathematics for Calculus - Seventh Edition

Ch. 11.1 - A parabola is the set of all points in the plane...Ch. 11.1 - The graph of the equation x2 = 4py is a parabola...Ch. 11.1 - The graph of the equation y2 = 4px is a parabola...Ch. 11.1 - Label the focus, directrix, and vertex on the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 6E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Prob. 8E Ch. 11.1 - Graphs of Parabolas Match the equation with the...Ch. 11.1 - Graphs of Parabolas Match the equation with the...

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To match: The polar equation r = 6 1 + cos θ with the graphs labeled I to VI.

Solution Summary: The author compares the polar equation r=61+mathrmcostheta with the graph II.

To match: The polar equation r=61+cosθ with the graphs labeled I to VI.

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Chapter 11 Solutions