Circles in general Show that the polar equation describes

Chapter 8, Problem 66E

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QUESTION:

Show that the polar equation

\(r^2-2r\ (a \cos \theta + b \sin \theta)\ =\ R^2-a^2-b^2\)

describes a circle of radius R centered at (a, b).

Questions & Answers

QUESTION:

Show that the polar equation

\(r^2-2r\ (a \cos \theta + b \sin \theta)\ =\ R^2-a^2-b^2\)

describes a circle of radius R centered at (a, b).

ANSWER:

Solution 66

Step 1:

The polar coordinates r and  can be converted to the Cartesian coordinates x and y by using the

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