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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
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 Directrix

Ellipse 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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