(I am second-guessing myself by asking this question.)

A parabola is created when a cutting plane passes through one nappe of a right double-cone (but not through the tip.)

To create a parabola, I believe that this cutting plane must beparallelto the side of the cone. I.e. - onlyoneangle for the cutting plane is possible.

Is this correct?

Most of the resources I have found don't specify the exact angle.

A circle is made if the cutting plane is perpendicular to the cone axis.

A hyperbola is created if the cutting plane goes through both nappes of the double cone,but doesn't have to be parallel to the cone axis.

An ellipse is created if the cutting plane goes through one nappe of the double-cone, but is not perpendicular to the cone axis.

Can a parabola be created if the cutting angle is within a particular angularrangewith respect to the perpendicular to the cone, or is it restricted toonly oneangle (parallel to the side of the cone)?

Can anybody recommend a resource that presents these properties and the specific angles (ranges) required to produce each type of conic?