The polar equation of the line perpendicular to the line $\sin \theta- \cos \theta=\large\frac{1}{r}$ and passing through the point $\bigg(2, \large\frac{\pi}{6}\bigg)$ is

Question

$(a)\;\sin \theta + \cos \theta=\frac{\sqrt 3+1}{r} \qquad (b)\;\sin \theta - \cos \theta=\frac{\sqrt 3+1}{r} \qquad (c)\;\sin \theta + \cos \theta=\frac{\sqrt 3-1}{r} \qquad (d)\;\cos \theta - \sin \theta=\frac{\sqrt 3}{r} $