I understand how conic sections are produced i.e. when a plane cuts a double nappe right circular cone at different angles, we get different types of conic sections like parabola, ellipse etc. But I don't understand how from this simple cutting (which I can visualize easily), they have derived the loci of these conics. For example :
A parabola is a locus of points equidistant from a single point, called the focus of the parabola, and a line, called the directrix of the parabola.
I really can't visualize why this locus should give me a parabola, or how they came up with this definition ?