Parabola is obviously given by two of its dots and by contact dotsdots in them. Ratio
For a line AC, where dot B ∈AC is defined ratio (ABC) = (B-A)/(C-B).
Let's assume that we have got given dots A, D and C and t ∈<0,1>. For dots E, B and F then it is valid : ratio (AED) = ratio (EBF) = ratio (DFC). Construction of a parabola lies in drawing a dot of parabola B with parameter r = t /(1-t).
Then 1. computes the point E, F : E : ratio(AED) = r ( <=> E = (1-t)*A + t*D ) F : ratio(DFC) = r ( <=> F = (1-t)*D + t*C ) 2. compute the point B : B : ratio(EBF) = r ( <=> B = (1-t)*E + t*F ) 3. The point B is the parabola with the corresponding parameter t