I've been doing some research into conic sections and I'm getting confused as to what the actual definition of the eccentricity of the conic section is.
Now from what I understand the eccentricity is defined as the ratio between the lengths FP and PD where F is the focus, P is the point and D is the perpendicular length to the directrix. I thought this applied to all conic sections.
I've also seen elsewhere as it being defined (for the ellipse) as: e=distance of focus from center/length of semi major axis
I'm sure it's a case of symmetry about the minor axis but I'm not sure where to start. Thank you for your help !