A limacon has a polar equation of the form and ,

where are positive.

Since the equation modeling this lollipop must be symmetric with respect to the line ,

the equation must have the form .

Since the lollipop appears to have an upside-down heart shape,  and the equation

has the form .

The fact that the lollipop measures  inches from the top of the lollipop to where the candy meets the stick tells us that , so .

Therefore, an equation that models this lollipop is .

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

The equation that models the lollipop is .