What is the conic section called when the eccentricity is 1? Why?

Actually NCERT book says that the definetion of eccentricity is c/a . where c is the distance b/w the two foci and a is the length of the major axis. hence when c= a the eccenricity becomes 1 and it forms a degenerate line.However all the reference books say that when the eccentricity is 1 it forms a parabola. Plz assist...