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?

There is also a single straight line and a point - both degenerate in the sense that the degree of the equation is less than $2$. 
You can consider the cone as cut by a family of parallel planes, and the conics on each plane will combine to give the whole cone. They will all be of the same type, with the plane through the apex giving a degenerate form.
You get a family of pairs of lines by considering cuts by the family of planes which contain the axis of the cone, and in this case all the "conics" are the same.
You can also consider a family of conics generated by the planes which contain a random line in space. In this case you will likely get all conics except a pair of lines (this only when the line goes through the apex, and consider a plane containing your line and the axis of the cone). You might miss a circle in cases where the plane through the apex is perpendicular to the axis and you get a point as a degenerate circle. Otherwise the apex gives you a degenerate ellipse.
