Solved: Tracing hyperbolas and parabolas Graph the

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567 2

Solution for problem 63E Chapter 10.4

Calculus: Early Transcendentals | 1st Edition

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Problem 63E

Tracing hyperbolas and parabolas Graph the following equations. Then use arrows and labeled points to indicate how the curve is generated as θ increases from 0 to 2π.

Step-by-Step Solution:

Solution 63E

Step 1:

In this problem we have to draw the graph of r = $\frac{3}{1\ -cos(\theta{})}$ and then use arrows and labeled points to indicate how the curve is generated as $\theta{}$ increases from 0 to 2 $\pi{}$ .

We know that the polar equation of parabola , with focus at origin , and opening along positive x-axis.

r = $\frac{2a}{1-cos(\theta{})}$ , where a = distance from focus to vertex.

The graph of r = $\frac{3}{1-cos(\theta{})}$ is shown below:

$\$

r = $\frac{3}{1-cos(\theta{})}$	$\theta{}$
r = $\frac{3}{1-cos(0)}$ = $\infty{}$	0 $\$ $\$
r = $\frac{3}{1-cos(\frac{\pi{}}{2})}$ = 3	$\frac{\pi{}}{2}$ $\$
r = $\frac{3}{1\ -cos(\pi{})}$ = $\frac{3}{2}$	$\pi{}$
r = $\frac{3}{1-cos(\frac{3\pi{}}{2})}$ = 3	$\frac{3\pi{}}{2}$
r = $\frac{3}{1-cos(2\pi{})}$ = $\infty{}$	2 $\pi{}$

As $\theta{}$ increases from 0 to 2 $\pi{}$ , the curve generated as a circle , and at $\theta{}$ = 0 and 2 $\pi{}$ the curve approaches to infinity.

Step 2 of 2

Chapter 10.4, Problem 63E is Solved

Textbook: Calculus: Early Transcendentals

Edition: 1

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

ISBN: 9780321570567

Since the solution to 63E from 10.4 chapter was answered, more than 270 students have viewed the full step-by-step answer. This full solution covers the following key subjects: arrows, curve, equations, generated, graph. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Tracing hyperbolas and parabolas Graph the following equations. Then use arrows and labeled points to indicate how the curve is generated as ? increases from 0 to 2?.” is broken down into a number of easy to follow steps, and 28 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 63E from chapter: 10.4 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM.