Let $A \subset \mathbb{R}^{n}$ be non-empty. The set $$ A^{\circ} = \lbrace c \in \mathbb{R}^{n} |\; \langle c,x \rangle \leq 1 \quad \forall x \in A \rbrace $$ is called the polar of $A$.
I'm trying to find the polar of $ \lbrace (x,y) \in \mathbb{R}^{2} |\; x^{2} + y^{4} \leq 1 \rbrace$.
I tried to take the function $f(x,y)=ax+by-1 \leq0$ and do a lagrange optimisation thing to try and find points $(a,b)$ subject to this constraint $g(x,y)=x^{2}+y^{4}-1$, but now I'm just confused and have no idea how to do this.
I don't know any advanced properties of polars, I only know a few basic ones and the bipolar theorem.
Any help would be appreciated.