Chapter 9: Q. 48 (page 772)

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \cos θ}$

Short Answer

Expert verified

The graph will be

Step by step solution

Step 1. Given Information.

The given equation is $r = \frac{2}{4 + \cos θ}$

Step 2. Comparison.

On comparing the given equation with standard form $r = \frac{e u}{1 + e \cos θ}$ ,

$r = \frac{\frac{2}{4}}{\frac{4 + \cos θ}{4}} r = \frac{\frac{1}{2}}{\frac{4}{4} + \frac{\cos θ}{4}} r = \frac{\frac{1}{2}}{1 + \frac{1}{4} \cos θ} The eccentricity e = \frac{1}{4} Here e u = \frac{1}{2} u = 2$

Step 3. Graph.

For $r = \frac{2}{4 + \cos θ}$ the eccentricity is $e = \frac{1}{4}$ , so the graph is an ellipse. The directrix will be the vertical line $x = 2 .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \cos θ}$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Comparison.

Step 3. Graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Use polar coordinates to graph the conics in Exercises 44–51.r=24+cosθ

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Comparison.

Step 3. Graph.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Logic and Functions

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Use polar coordinates to graph the conics in Exercises 44–51.
$r = \frac{2}{4 + \cos θ}$