Multicolinearity, two explanatory variables

Problem

In the model \(y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+ε_i\) assuming random sample and GM, one can show that

\[Var\left( b_2|x \right)= \frac{σ^2}{\sum_{i}^{n}{ {\left( x_{i,2}-{\bar{x}}_2 \right)}^2 }} \frac{1}{1-ρ_{1,2}^2}\]

where \(ρ_{1,2}^2\) is the (true) correlation between \(x_{i,2}\) and \(x_{i,3}\) (which is the same for all \(i\) due to random sampling).

In terms of the parameters presented, what do we mean by perfect multicolinearity?

Is there a way of formally defining multicolinearity in terms of the parameters presented?