   Chapter 10, Problem 55RE

Chapter
Section
Textbook Problem

# Find a polar equation for the ellipse with focus at the origin, eccentricity 1 3 , and directrix with equation r = 4 sec θ.

To determine

To find: The polar equation of the curve with focus at the origin, and an eccentricity value of (13) are to be found. The directrix line for the equation r=4secθ is to be derived.

Explanation

Given:

The expression for the eccentricity is as below.

e=(13) (1)

The expression for the directrix is as below.

r=4secθ

Calculation:

Simplify the directrix equation r=4secθ .

r=4secθr=4cosθ

rcosθ=4rcosθ=x

x=4

The directrix equation is given as below.

d=4 (2)

Determine the polar equation of the ellipse using the formula

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