Let $F_p$ be a finite field and $p\equiv 3 \pmod 4$, and $a,c$ are non-square elements in $F_p$. I want to parametrize the conic:

$$cy^2=-3x^2-2ax-16a$$

($-1$ and $3$ are non-squers in this field as well). Would you please help me to do that. Thanks