The given polar equation is r = 4 + 2cos(theta).
The type of limaçon graphed by this polar equation is a cardioid.
The axis of symmetry is the polar axis (horizontal axis).
The horizontal intercepts occur when r = 0, so we have 0 = 4 + 2cos(theta), which gives cos(theta) = -2. Since the cosine function is bounded between -1 and 1, there are no real solutions for theta, meaning there are no horizontal intercepts.
The vertical intercepts occur when theta = 0 or theta = pi, giving us r = 4 + 2cos(0) = 6 and r = 4 + 2cos(pi) = 2, respectively. Therefore, the vertical intercepts are at (6, 0) and (2, pi).
What type of limaçon is graphed by the polar equation ? Identify the axis of symmetry and horizontal and vertical intercepts. (4 points)
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