Answer:
Correct option is C ) [tex]r=3+2\,cos\theta[/tex]
Step-by-step explanation:
Limacons are polar functions of the type:
[tex]r=a\pm\,b\,cos\theta[/tex]
[tex]r=a\pm\,b\,sin\theta[/tex]
Where [tex]|\frac{a}{b}|<1\,or\,1<|\frac{a}{b}|<2\,or\,|\frac{a}{b}|$\geq$2[/tex]
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, [tex]r=3+2\,cos\theta[/tex] satisfies the condition of graph.
hence correct option is c ) [tex]r=3+2\,cos\theta[/tex] .
