Question

A polar equation is given as r = 3 + 2cos(0). Based on the relationship
between the coefficients, which type of limaçon does this represent, and what is the significance of this classification?
* 1 point
A dimpled limaçon, because the coefficient of cos®) is less than the constant term, creating an indentation
• A rose curve, because the equation contains a cosine function with a coefficient
• A cardioid, because the constant term equals twice the coefficient of cos(e)
A convex limaçon, because the constant term is greater than the coefficient of cos(e), eliminating any indentation

Answer 1

Correct answer: A dimpled limaçon.

Reason: For r = a + b cosθ with a = 3 and b = 2, a/b = 3/2 = 1.5, which lies between 1 and 2. That range produces a dimpled limaçon — the curve has an indentation (a “dimple”) but no inner loop. (If a/b = 1 it would be a cardioid; a/b < 1 gives an inner loop; a/b ≥ 2 gives a convex limaçon.)