Problem #9: an ellipse problem

ABSTRACT

The problem concerns four variables a,b,c,d to be interpreted as centre (c,d) and principal semiaxes a,b of an ellipse [EQUATION] We wish to know when E lies inside the unit disk D: x² + y² ≤ 1. More precisely, we seek a set of polynomials {Pj(a², b², c², d²,)} for j=1,2,...,n with the property that E≤Dif and only if all Pj(a², b², c², d²,) ≤0. It is known that n> 1, but n should be minimal.