Question

Determine which equation is belongs to the graph of the limacon curve below.

Answer 1

Answer:

Correct option is C ) $r=3+2\,cos\theta$

Step-by-step explanation:

Limacons are polar functions of the type:

$r=a\pm\,b\,cos\theta$

$r=a\pm\,b\,sin\theta$

Where $|\frac{a}{b}|$

In provided options part (a) and (d) constants 'a' and 'b' does not satisfied the condition,

in part (b) and (c) both satisfies the condition but in part (b) we get loop  inside the sketch.

so,  $r=3+2\,cos\theta$ satisfies the condition of graph.

hence correct option is c )  $r=3+2\,cos\theta$ .

Answer 2

Answer:

c. 3 + 2 cosθ

Step-by-step explanation:

a = 3, b = 2

Since a > b, 1 < $\frac{3}{2}$ <2

we get a dimpled limacon.