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CalculusCalculus10th Edition

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Chapter 10.6, Problem 15E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Sketching and Identifying a Conic In Exercises 13–22, find the eccentricity and the distance from the pole to the directrix of the conic. Then sketch and identify the graph. Use a graphing utility to confirm your results.

r = 3 2 + 6   sin   θ

To determine

To Calculate:

The eccentricity and distance from the pole to the directrix of the conic r=74+8sinθ 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=74+8sinθ.

Formula Used:

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

Calculation:

The given equation is: r=74+8sinθ

And the equation can be re-written as,

r=78×21+2sinθ

Compare this equation with the standard equation r=ed1+esinθ to get the Eccentricity as e=2 and the distance as d=78.

Here e>1, hence the curve for the given equation is hyperbola.

Hence, the distance of directrix from the pole is d=78.

Graph:

The given equation is of hyperbola since e>1.

To draw the graph of hyperbola plot some points by taking different values for θ as in the table shown below

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Chapter 10.6,
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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Finding the Angle Between Two Vectors In Exercises 23 and 24, find the angle between the vectors (a) in radian...

Multivariable Calculus

This exercise requires use of a statistical software package. Using a statistical computer package, compare the...

Introduction To Statistics And Data Analysis

Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on ...

Statistics for Business & Economics, Revised (MindTap Course List)

In Exercises 33-54, solve the given equation. The solution of every other odd-numbered exercise is given in the...

Mathematics: A Practical Odyssey

In Exercises 11 and 12, express the given fractions as equivalent fractions with the indicated denominators. 12...

Mathematics For Machine Technology

What pattern of results is needed to provide convincing evidence that behavior changed when the phase was chang...

Research Methods for the Behavioral Sciences (MindTap Course List)

The following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In addition to the key words, you should also be able to define the following terms: Third-variable problem Pla...

Research Methods for the Behavioral Sciences (MindTap Course List)

Write an equation of each circle shown or described. Write your answer in standard form and then general form.

College Algebra (MindTap Course List)

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