   Chapter 10.6, Problem 6E

Chapter
Section
Textbook Problem

# Writing Consider the polar equation r = 4 1 − 0.4   cos   θ . (a) Identify the conic without graphing the equation.(b) Without graphing the following polar equations, describe how each differs from the polar equation above. r = 4 1 − 0.4   cos   θ , r = 4 1 − 0.4   sin   θ (c) Verify the results of part (b) graphically.

(a)

To determine

The conic for the polar equation, r=410.4cosθ without graphing it.

Explanation

The polar form of conic is given by the equations,

r=ed1±ecosθ or r=ed1±esinθ

Where, e is the eccentricity of the conic and d is the distance between focus and pole

(b)

To determine

The nature for the polar equations, r=41+0.4cosθ and r=410.4sinθ without graphing it.

(c)

To determine

To graph: The polar equations, r=41+0.4cosθ and r=410.4sinθ to verify the graphs are elliptical and the directrix of r=41+0.4cosθ lies to the right of the pole and the directrix of r=410.4sinθ lies below the pole.

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