Explanation Draw the conic for the given polar equation as shown below in Figure 1. From Figure 1, it can be noted that the distance | P l | = d − r cos α and P F = r . From a theorem it is known that if F is a fixed point and l be a fixed line in a plane. Let e be a fixed positive number. The set of all points P in the plane such that | P F | | P l | = e is a conic section . Substitute | P l | = d − r cos α and P F = r in | P F | | P l | = e as, e = | P F | | P l | e = r d − r cos α e = r d − r cos ( π − θ )

9th Edition

ISBN: 9781337613927

Author: Stewart

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Question

Chapter 10.6, Problem 27E

To determine

To show: The conic with focus at the origin, eccentricity and directrix x=−d has polar equation r=ed1−ecosθ.

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Chapter 10.6, Problem 26E

Chapter 10.6, Problem 28E

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The conic with focus at the origin, eccentricity and directrix x = − d has polar equation r = e d 1 − e cos θ .

Solution Summary: The author illustrates the polar equation r=ed1-emathrmcostheta in Figure 1.

To show: The conic with focus at the origin, eccentricity and directrix x=−d has polar equation r=ed1−ecosθ.

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Chapter 10 Solutions