   Chapter 10.6, Problem 5E

Chapter
Section
Textbook Problem

# Writing Consider the polar equation r = 4 1 + e   sin   θ . (a) Use a graphing utility to graph the equation for e = 0.1, e = 0.25, e = 0.5, e = 0.75, and e = 0.9. Identify the conic and discuss the change in its shape as e → 1– and e → 0+.(b) Use a graphing utility to graph the equation for e = 1. Identify the conic.(c) Use a graphing utility to graph the equation for e = 1.1, e = 1.5, and e = 2. Identify the conic and discuss the change in its shape as e → 1+ and e → ∞.

(a)

To determine

To graph: The polar equation r=41+esinθ for e=0.1,e=0.25,e=0.5,e=0.75 and e=0.9 and with the help of graphing utility and then identify which conic is represented by the given conditions and discuss the change in shape of conic as e1 and e0+.

Explanation

Given:

The polar equation is r=41+esinθ and the conditions are,

e=0.1,e=0.25,e=0.5,e=0.75 and e=0.9.

Graph:

Consider the polar equation,

r=41+esinθ

The polar equation can be drawn with the help of graphing utility in Maple as shown below:

As observed from the graph the conic is an ellipse

(b)

To determine

To graph: The polar equation r=41+esinθ for e=1 with the help of graphing utility and then identify which conic is represented by the given condition.

(c)

To determine

To graph: The polar equation, r=41+esinθ when e=1.1,e=1.5 and e=2 and then identify which conic is represented by the given conditions and discuss the change in shape of conic as e1+ and e.

### 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

#### 61/2

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

#### Differentiate the function. f(x) = e5

Single Variable Calculus: Early Transcendentals, Volume I

#### The graph of x = cos t, y = sin2 t is:

Study Guide for Stewart's Multivariable Calculus, 8th

#### limh0ah1h=1 for a = a) 0 b) 1 c) e d) The limit is never 1.

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

#### Factor each polynomial. x6-1

College Algebra (MindTap Course List) 