This is probably a really obvious question, but I don't see the explanation.

We have a population of $(X, Y)$ pairs for which $\rho_{XY}=\rho$ and $Y$ is given by the linear representation $Y = \alpha + \beta X + e$ where $\operatorname{Cov}(X,e) = 0$.

What is the best linear representation of the relation between $Y$ and $X$ with the variables reversed: $X = \gamma + \delta Y + u$. Specifically what would $\delta$ be in terms of $\alpha$ and $\beta$?