What is the polar of an Euclidean unit ball but its center is not in the origin

356 Views Asked by At

I know that the polar of an Euclidean unit ball is itself, but I wonder what if its center is not in the origin, like: $$ B=\{(x,y)\in \mathbb R^2 \mid(x-1)^2+y^2\le1\} $$ and the polar of a set is: $$ B^{\circ} = \{ c \in \mathbb{R}^{n} \mid \langle c,x \rangle \leq 1 \quad \forall x \in B \} $$ Please show me some details, thank a lot!!