Question

If you need to write a polar equation for a limaçon that passes through the * 1 point point (5, 0) in polar coordinates and has a dimple on the right side, which equation would be most appropriate?
0 r= 2 + 5cos(e), because the constant term determines the maximum distance from
the origin
r = 5sin(e) + 3cos(e), because it combines both trigonometric functions for greater
control
r = 5 + 3sin(®), because it ensures the curve passes through (5, 0) regardless of the angle
r = 3 + 2cos(0), because it creates a dimpled limaçon with maximum r-value of 5 at 0
= 0

Answer 1

r = 3 + 2 cos(θ).

Reason: for a limaçon r = a + b cos θ you need a + b = 5 to pass through (5,0). A dimple occurs when 1 < a/b < 2. With a = 3 and b = 2 we have a + b = 5 and a/b = 3/2 (between 1 and 2), and the cos form places the dimple on the right side. The other choices fail one or both conditions.