Chapter 10.6, Problem 15E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Identifying and Sketching a Conic In Exercises 13-22, find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm your results. r = 7 4 + 8 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+8sinÎ¸.

Formula Used:

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

Calculation:

The given equation is: r=74+8sinÎ¸

And the equation can be re-written as,

r=78Ã—21+2sinÎ¸

Compare this equation with the standard equation r=ed1+esinÎ¸ 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

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