Ellipse implicit equation

Testing congruence between an ellipse defined as a graphical object and an ellipse defined as an implicit equation. The dotted black ellipse is drawn using standard drawing operations, the colours are the result of mapping the outcome of the Eq(x,y) equation shown onto two gradients (one for negative values, ie. on the interior of the ellipse, one for positive values, ie. the exterior of the ellipse).

With an ellipse equation it becomes cheap to evaluate inside/outside relationships and even a kind of 'how much inside/outside'. This in turn will be useful when resampling grids (for example when resizing/rotating/deforming images), or when shooting rays+error cones at textures.