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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Section
BuyFindarrow_forward

Calculus

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

Identifying a Conic In Exercises 23-26, use a graphing utility to graph the polar equation. Identify the graph and find its eccentricity.

r = 10 1 cos θ

To determine

To Calculate:

The sketch of the polar equation r=101cosθ using graphing utility and identify the graph and also find its eccentricity.

Explanation

Given: The provided polar equation is r=101cosθ.

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:

Consider the polar equation of conic as: r=ed1ecosθ

Here e is eccentricity and d is distance between focus at pole and corresponding directrix.

The equation can be re-written as,

r=10(11.cosθ)

Compare it with the standard equation to get,

e=1

Hence, for e=1, the conic is parabola.

Graph:

Use Desmos graphing calculator and write the equation to plot the following graph:

To sketch the graph of a parabola, plot some points by taking different values for θ as in the table

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Chapter 10 Solutions

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