Let a and b be real numbers. Describe the graph of r = a(cos(theta)+b) as much as possible.
(The intent of this question is to get as specific a description as possible that holds for all possible values of a and b.
For example, if the question was to describe the graph of x^2/a^2 + y^2/b^2 = 1, then a suitable answer is an ellipse that is centered at the origin. The answer "an ellipse" would not be "as specific as possible" for this ellipse example.)
Im having trouble thinking about this problem. Any help?
r = a cosθ + b
This is certainly not an ellipse.
Play around some at wolframalpha.com
For example, enter
r = 2cosθ+2
and see the graph. Then mess around with a and b, positive and negative, with various ratios. The graph can have several distinct qualities.
Read up on cardioids.