The maximum number of common normals to ${\mathrm{y}}^2=4\mathrm{ax}$ and ${\mathrm{x}}^2=4\mathrm{by}$ may be ____

$$\begin{gathered} Equations of normals to given parabolas are \\ y+xt=2at+a{t}^3\to \left(i\right) \\ x+ys=2bs+b{s}^3\to \left(ii\right) \\ \sin ce \left(i\right) and \left(ii\right) represents same then \\ \frac{t}{1}=\frac{1}{s}=\frac{2at+a{t}^3}{2bs+b{s}^3} \\ \Rightarrow ts=1 and 2a+t^2=2bs+b{s}^3 \\ \Rightarrow b{s}^5+2b{s}^3-2a{s}^2-a=0 \\ \mathrm{Maximum} \mathrm{possible} \mathrm{common} \mathrm{normals}=5 \end{gathered}$$