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: sin 0 = 0 , sin π 2 = 1 , sin π = 0 , sin 3 π 2 = − 1 Calculation: The given polar equation of conic is r = 5 3 − 3 sin θ . It can be written as r = 5 3 1 − sin θ (1) Compare the equation (1) with r = e d 1 − e sin θ by definition stated above, it is observed that, e = 1 and d = − 5 3 . That is, directrix is y = − 5 3 . That is equation (1) is a parabola opens upward. From the set graphs it is observed that the graph I is the only graph representing opens upward. To conclude that the equation 1 matches graph I, 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 = 5 3 1 − sin 0 = 5 3 1 − 1 = ∞ When θ = π 2 , the value of r is computed as follows. r = 5 3 1 − sin π 2 = 5 3 1 − 0 = 5 3 When θ = π , the value of r is computed as follows

Rutgers University Precalculus Mathematics for Calculus 640: 111/112/115 + Enhanced Web Assign Printed Access Card BNDL

7th Edition

ISBN: 9781305743847

Author: Stewart/Redlin/Watson

Publisher: Cengage Learning

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Chapter 11.6, Problem 14E

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To match: The polar equation r=53−3sinθ with the graphs labeled I to VI.

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Chapter 11.6, Problem 13E

Chapter 11.6, Problem 15E

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Chapter 11 Solutions

Rutgers University Precalculus Mathematics for Calculus 640: 111/112/115 + Enhanced Web Assign Printed Access Card BNDL

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 = 5 3 − 3 sin θ with the graphs labeled I to VI.

Solution Summary: The author compares the polar equation of a conic with focus at the origin and the directrix with the graphs labeled I to VI.

To match: The polar equation r=53−3sinθ with the graphs labeled I to VI.

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Chapter 11 Solutions