   Chapter 10.6, Problem 18E

Chapter
Section
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 = 10 5 + 4 sin θ

To determine

To Calculate:

The eccentricity and distance from the pole to the directrix of the conic for the given equation r=105+4sinθ 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=105+4sinθ

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=105+4sinθ

And the equation can be re-written as,

r=105(1+45sinθ)

r=45×521+45sinθ

Compare this equation with the standard equation r=ed1+esinθ to get the eccentricity as e=45 and the distance as d=52

Here e=45<1, hence the curve is ellipse

And the distance of directrix from the pole is d=52

Graph:

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

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