bathtub and shower on one p-trap?

I am remodeling a bathroom to add a shower and replace the old tub. The existing p-trap for the tub does not line up with the tub drain as is conventionally shown. It is offset about 12 inches. My question is can I connect the new shower pan and the new bathtub to the same (existing) p-trap. The arrangement would be shower pan, and tub tee'ed into the p-trap, then vent, and then drain to the septic tank.
The structure is concrete slab. The water level in the p-trap is about 9 inches below the current slab floor surface so both fixtures would be above the p-trap water level.

No, each item must have its own trap AND vent.

Jim, thank you.
How is this different from a double sink that shares a common p-trap and vent?

IT differs because they are TWO DIFFERENT fixtures, not a single one with two bowls. A two bowl sink has a single faucet, so even if two people were using the sink, only one could be using the water at any given time. That is not true of a shower and tub where two people could be using them simultaneously. In addition, connecting them together would provide an air flow path which could cause an odor problem.