Answered: Solve, a. Identify the conic section…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.9: Polar Equations Of Conics

Problem 3ECP

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Question

Solve, a. Identify the conic section that teh polar equation r = 12/(2 - 4cos θ) represents. b. Describe the location of a directrix from the focus located at the pole.

Expert Solution

Step 1

Concept:

The calculus helps in understanding the changes between values that are related by a function. It is used in different areas such as physics, biology and sociology and so on. The calculus is the language of engineers, scientists and economics.

Step 2

Given:

$r = \frac{12}{2 - 4 \cos θ}$ $r = \frac{6}{1 - 2 \cos θ}$

Step 3

(a)

The constant term in the denominator is not 1. So the given equation is not in standard form.

Dividing the numerator and denominator by 2 to get the equation in standard form

$r = \frac{6}{1 - 2 \cos θ}$

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