Circle, ellipse, parabola and hyperbola When the plane cuts the nappe (other
than the vertex) of the cone, we have the following situations:

(a) When β = 90o

, the section is a circle (Fig11.4).

(b) When α < β < 90o
, the section is an ellipse (Fig11.5).

(c) When β = α; the section is a parabola.

(In each of the above three situations, the plane cuts entirely across one nappe of

the cone).

(d) When 0 ≤ β < α; the plane cuts through both the nappes and the curves of

intersection is a hyperbola