If $\frac{X_a}{X_a+Y_a}$ and $\frac{X_b}{X_b+Y_b}$ are correlated, what about $X_a+Y_a$ and $X_b+Y_b$

Question

Suppose I have four normal random variables:$X_a$,$Y_a$,$X_b$,$Y_b$.

$X_a$ and $Y_a$ follow bivariate normal, $X_b$ and $Y_b$ also follow bivariate normal.

let $Z_a=\frac{X_a}{X_a+Y_a}$ , $Z_b=\frac{X_b}{X_b+Y_b}$ and $Z_a*Z_b=p$, p is a known constant.

Can I calculate the correlation between $X_a+Y_a$ and $X_b+Y_b$