   Chapter 10.6, Problem 47E

Chapter
Section
Textbook Problem

Finding a Polar Equation Find a polar equation for the ellipse with the following characteristics.Focus: (0, 0)Eccentricity: e = 1 2 Directrix: r = 4 sec θ

To determine

To calculate: A polar form of the equation for the ellipse having the focus (0,0), Eccentricity e=12, the equation of directrix r=4secθ.

Explanation

Given:

The conic is a ellipse having:

Focus (0,0)

Eccentricity e=12

Directrix r=4secθ

Formula used:

The polar form of the equation for the ellipse having its focus at the pole is:

r=ed1+ecosθ

Here e is the eccentricity and d is the distance from the focus to its directrix.

Calculation:

Consider the directrix equation and convert it into the rectangular form,

r=4secθr=4cosθrcosθ=4

Since x=rcosθ

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