Answer:
A
Step-by-step explanation:
A limacon curve passes trough the point [tex]\left(\dfrac{\pi}{2},0\right)[/tex], this means when [tex]\theta =\dfrac{\pi}{2},[/tex] the distance [tex]r=0.[/tex]
Note that
[tex]\sin \dfrac{\pi}{2} =1,[/tex]
so, if [tex]r=a+b\sin \theta,[/tex]
then
[tex]r\left(\dfrac{\pi}{2}\right)=a+b=0\\ \\a=-b[/tex]
The only option which shows a = -b is option A.
