General Polar Equation of a Circle Problem: The general polar equation of a circle that

Chapter 13, Problem C3

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General Polar Equation of a Circle Problem: The general polar equation of a circle that does not pass through the pole can be found with the help of the law of cosines. Suppose a circle of radius a is centered at the point with polar coordinates (k, ), as shown in Figure 13-6g. Figure 13-6g a. Use the law of cosines to write an equation relating r, a, k, and the angle ( ). Solve the equation for r with the help of the quadratic formula. b. The quadratic formula has an ambiguous sign in it. Use the form of the solution with the + sign to plot the circle with radius 3 centered at (7, 40). Use a -range of 0 to 360. Does the grapher plot the graph as one continuous circle? c. Use the equation for r that has the sign. How does the graph relate to the one in part b? d. Find the two values of r if = 50. e. Show algebraically that there are no values of r if = 90.