It seems desirable that the methods taught to beginners of reducing the general equation of the second degree to the standard forms should be based on elementary properties of conics directly deduced from the standard equations. The methods given below are suggested as being simpler than those indicated in textbooks or in the references quoted below. It is presumed that pupils are already conversant with the forms and names of the conics represented by the equations (x/p)2±(y/q)2= 1, y2 = 4nx, of the existence of the centre and axes of symmetry (principal axes) of the central conics, and of the axis and the tangent at the vertex of the parabola. No other property of the conic is assumed.