Chapter 10, Problem 118RE

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Identifying and Sketching a Conic In Exercises 113-118, find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm y our results. r = 8 2 − 5 cos θ

To determine

To calculate: The eccentricity and the distance between the pole and the directrix of the conic r=825cosθ. Then identify the type of conic and sketch the graph of the conic r=825cosθ. Use graphing utility to confirm the results.

Explanation

Given:

The polar equation is r=82âˆ’5cosÎ¸.

Calculation:

Consider the equation:

r=82âˆ’5cosÎ¸

The standard equation of a conic with eccentricity e and distance between the pole and the directrix d is:

r=ed1+ecosÎ¸

Multiply and divide the fraction by 2. Then,

r=822âˆ’5cosÎ¸2

So,

r=41âˆ’52cosÎ¸

Compare the given equation with the standard equation r=ed1+ecosÎ¸, ed=4 and e=52

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