Elements of the form $aX^2 + bY^2$ in a finite field.

Question

For cardinality reasons, we know that every element in a finite field $F$ is a sum of two squares. If I fix $a,b\in F$ with $a,b\neq 0$, can every element in $F$ be written in the form $aX^2 + bY^2$ for some $X,Y$ in $F$? If not, can we say how many solutions there are in terms of $a$ and $b$?