It's funny... I'm almost 40, and I'm pretty sure I must have missed the day in high school math where Conic Sections were described this way. A couple of months ago I saw an almost identical diagram and had this "aha!!!" moment. I've worked with the abstract equations my entire career and have had no problem with it, but the visual aid really helped understand why they're called that and where they come from. More likely, though, than it being useful for understanding the nature of the different conic sections, it'll be more useful for understanding trajectories on a cone at some point :)