Chapter 10.6, Problem 25E

### 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 a Conic In Exercises 23-26, use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity. r = − 10 1 − cos θ

To determine

To Calculate:

The sketch of the polar equation r=101cosθ using graphing utility and identify the graph and also find its eccentricity.

Explanation

Given: The provided polar equation is r=âˆ’101âˆ’cosÎ¸.

Formula Used:

For the equation of the type r=ed1+esinÎ¸, e is the eccentricity and d is the distance between focus at pole and corresponding directrix.

Calculation:

Consider the polar equation of conic as: r=âˆ’ed1âˆ’ecosÎ¸

Here e is eccentricity and d is distance between focus at pole and corresponding directrix.

The equation can be re-written as,

r=âˆ’10(1âˆ’1.cosÎ¸)

Compare it with the standard equation to get,

e=1

Hence, for e=1, the conic is parabola.

Graph:

Use Desmos graphing calculator and write the equation to plot the following graph:

To sketch the graph of a parabola, plot some points by taking different values for Î¸ as in the table

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