   Chapter 10.6, Problem 35E

Chapter
Section
Textbook Problem

# Finding a Polar Equation In Exercises 33-38, Find a polar equation for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form)Conic Eccentricity DirectrixEllipse e = 1 4 y = 1

To determine

To calculate: The polar equation for the ellipse having its focus at the pole the eccentricity e=14 and the equation of directrix is y=1.

Explanation

Given:

The conic is ellipse having

The eccentricity is: e=14

And the equation of directrix is y=1

Formula used:

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

r=ed1+esinθ

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

The standard equation of directrix is y=d

Calculation:

The equation for directrix is y=1

So,

y=dd

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