Does a right circular cone only consists of pair of straight lines, hyperbolas, parabola, circles and ellipses? I was reading about the conic sections and that a conic section includes pair of straight lines, ellipses, hyperbola, circles and parabola.
Are all these 5 components enough to form a right circular cone or are these just the parts of right circular cone? What I mean is : if I put together infinite number of circles, parabolas, hyperbolas,, ellipses and circles, will I get a right circular cone?

A cone is a surface and as such cannot consist of a finite number of curves.
A conic section is the intersection of a cone with a plane, so it is a planar curve. Depending on the relative positions of the cone and the plane, the section can be a single or a double line, an ellipse, a parabola or an hyperbola (the circle is just a particular case of the ellipse).
A way to reconstruct a cone is to sweep a plane over the whole space (for instance by translation or rotation), a put together all the sections so obtained.
Putting together random lines, ellipses... in any number will just result in a mess.
