Critique of constant ratio property

The discovery of directrices and eccentricity leads us to quite a few questions:

• The eccentricity of an ellipse is always less than 1, being 0 for a circle. Does it make sense to talk about a negative eccentricity? Is the eccentricity of a parabola 1 and of a hyperbola more than 1?
  
  
• Given an ellipse, how can we find its foci and directrices? Can they be constructed with straightedge and compass?
  
  
• How far are the directrices from the foci? Where are the directrices of a circle?
  
  
• And our ongoing question: What are analogies for ellipses of properties of the circle like the perpendicularity of radii and tangent lines, the equation, the circumference formula, and the area formula?