ellipse

Let $$P = \left[ {\matrix{ 3 & 1 \cr 1 & 3 \cr } } \right].$$ Consider the set $$S$$ of all vectors $$\left( {\matrix{ x \cr y \cr } } \right)$$ such that $${a^2} + {b^2} = 1$$ whe...

If at every point of a certain curve , the slope of the tangent equals $${{ - 2x} \over y},$$ the curve is _______.