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Solved: Circles in general Show that the polar equation
Chapter 8, Problem 67E(choose chapter or problem)
QUESTION:
Show that the polar equation
\(r^2-2rr_0 \cos\ (\theta-\theta_0)=R^2-r^2_0\)
describes a circle of radius R whose center has polar coordinates \((r_0,\ \theta_0)\).
Questions & Answers
QUESTION:
Show that the polar equation
\(r^2-2rr_0 \cos\ (\theta-\theta_0)=R^2-r^2_0\)
describes a circle of radius R whose center has polar coordinates \((r_0,\ \theta_0)\).
ANSWER:Solution 67E
Step 1:
The polar coordinates r and can be converted to the Cartesian coordinates x and y by using the trigonometric functions sine and cosine:
Given: (Using