Assume that $ab \neq 0$. What is $$N_p := \text{card}\{(x, y, z, t) \in (\textbf{F}_p)^4 : ax^4 + by^4 + z^2 + t^2\}?$$I need this result, but unfortunately I am not a number theorist. Could anyone provide me a reference/supply a computation? Thanks!