Another basement bathroom....

[mitchdandy]

I'm adding a basement toilet and sink, to a house I'm selling. The connection I am planning is between the main 4" vertical stack and the central line running to the sewer. I'm looking for the appropriate "distance to vertical stack" for toilet venting. I'm under the impression I could use the current stack for this toilet provided it was within "x". Next, the 1 1/2"-2" sink line could Y off of the toilet or cut into the central line. I was going to use a studor valve for the sink.
Am I pretty close?