   Chapter 10, Problem 120RE

Chapter
Section
Textbook Problem

# Finding a Polar Equation In Exercises 119-122, find a polar equation Tor the conic with its focus at the pole and the Risen eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)Conic Eccentricity DirectrixEllipse e = 3 4 y = − 2

To determine

To calculate: With the given eccentricity and directrix, find a polar equation for the conic for which the focus is at the pole. (For convenience, the rectangular form of the directrix equation is given.)

Explanation

Given: Conic: Ellipse, Eccentricity: e=34 and Directrix: y=2

Calculation: A conic with eccentricity e=34 and directrix y=2 are given.

Also, since the focus is at the pole, d=2.

Here, the directrix is a line parallel to the x-axis. Therefore, the standard equation of the conic is

r=ed1esinθ

Substitute for e and d.

Then,

r=(34)(2)1(

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