No, formula is ALWAYS the same. That was a formula for double the point:
c = 3*P.x*Px*invert(2*P.y) % modulo
R.x = (c*c - 2*P.x) % modulo
R.y = (c*(P.x - R.x) - P.y) % modulo

If you want to add 2 points P and Q (2 different non-zero Points) there is another formula for R = P + Q:
dx = (Q.x - P.x) % modulo
dy = (Q.y - P.y) % modulo
c = dy * invert(dx) % modulo
R.x = (c*c - P.x - Q.x) % modulo
R.y = (c*(P.x - R.x) - P.y) % modulo