How to compute correlation from variances

You have two random variables $X$ and $Y$.

You are told:

• $\mathrm{Var}(X+Y)$
• $\mathrm{Var}(X)$

1. Is this information sufficient to determine the correlation $\rho_{X,Y}$ ? If not, what additional quantity(ies) would you need?
2. If you also know $\mathrm{Var}(Y)$ , derive $\rho_{X,Y}$ in terms of $\mathrm{Var}(X+Y)$ , $\mathrm{Var}(X)$ , and $\mathrm{Var}(Y)$ .
3. Special case: if you assume $\mathrm{Var}(Y)=\mathrm{Var}(X)$ , simplify the expression for $\rho_{X,Y}$ .