Chapter 10.6, Problem 16E

### 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 13-22, 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 your results. r = 4 1 + cos θ

To determine

To Calculate:

The eccentricity and distance from the pole to the directrix of the conic given by the equation r=41+cosθ and identify the conic. Also, sketch its graph and confirm the results with that of the graphing utility

Explanation

Given: The polar equation is given as r=41+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:

The given equation is: r=41+cosÎ¸

And the equation can be re-written as,

r=4Ã—11+1cosÎ¸

Compare this equation with the standard equation r=ed1+ecosÎ¸ to get the eccentricity as e=1 and the distance as d=4.

Here e=1, hence the curve for the given equation is parabola.

Hence, the distance of directrix from the pole is d=4

And the equation of directrix is x=âˆ’4.

Graph:

Since e=1, hence the curve for the given equation is parabola

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

## Additional Math Solutions

#### Find the limit or show that it does not exist. limxx2x2+1

Single Variable Calculus: Early Transcendentals, Volume I

#### In Exercises 107-120, factor each expression completely. 116. (x + y)2 1

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Read each scale:

Elementary Technical Mathematics

#### Calculate y'. 1. y = (x2 + x3)4

Single Variable Calculus: Early Transcendentals

#### Find for defined implicity by .

Study Guide for Stewart's Multivariable Calculus, 8th

#### For y=12gt2 (where g is a constant), dydt=. a) 14g2 b) 12g c) gt d) gt2

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Define and compute the three measures of central tendency.

Research Methods for the Behavioral Sciences (MindTap Course List)