I have been reading about conic sections lately.
I read that a conic section is the sections obtained when a double napped right circular cone is cut through by a plane at a particular angle with respect to its axis. This definition of the term conic section justifies the name. Depending on the angle between the axis of the double napped right circular cone and the cutting plane, conic sections can be classified into many types.
Now, later on i read another definition that a conic section is defined as the locus of a point moving in a plane such that the ratio of the distance of the point from a fixed point in that plane (focus) to the perpendicular distance of the point from a fixed straight line in the plane (directrix) is a constant (eccentricity). Based on the value of the eccentricity, the conic section can be classified into many types.
I cannot understand the relation between the two definitions. How did this second definition arise. Please help.
P.S.: I was browsing this site for similar questions. I found one question which seemed similar to mine by the title but on reading the question details i found that my question is a bit different.
