Question

NEED HELP ASAP. 20 POINTS!!! The graph of a limacon curve is given. Determine which equation is correct for the graph.

Answer 1

Answer:

The equation r = 3 - cos Ф is correct for the graph ⇒ 3rd answer

Step-by-step explanation:

Equations of the form r = a + b sin Ф, r = a - b sin Ф, r = a + b cos Ф, and r = a - b cos Ф represent limacons

• Equations r = a + b sin Ф, r = a - b sin Ф are symmetric to the vertical axis
• Equations r = a + b cos Ф, r = a - b cos Ф are symmetric to the horizontal axis
• The shape of the limacons depends on the values of a and b

∵ The figure is a circle

- That means a is greater than twice b

∴ a > 2b

∵ The circle is symmetric to the x axis

∵ The majority of the circle lies in quadrants two and three

- That means most of the graph at the negative part of x

∴ The form of the equation is r = a - b cos Ф

Lets look to the answer to find the right one

∵ a > 2b

∴ a = 3 and b = 1 because 3 > 2(1)

∴ The answer is r = 3 - cos Ф

The equation r = 3 - cos Ф is correct for the graph