The authors show that the boundary of the polar set $E^{\land}$ of the 
sum $E$ of $k$ elliptical discs $E_1, \ldots, E_k$  with center at the 
origin lies on an algebraic curve $C$ of degree $2^k$. The authors 
give an algorithm to compute the defining polynomial of $C$ and apply 
it to $k$-numerical range and a problem in Architecture.