When you derive from DbContext and use the parameter-less constructor it will load a connection string from web.config. You also have the option of explicitly specifying the
Create your DbConnection manually and pass it to the DbContext constructor as follows:
var conn = DbProviderFactories.GetFactory("MY_CONN_PROVIDER").CreateConnection();
conn.ConnectionString = "MY_CONN_STR";
new DbContext(conn, true);
Notice the second parameter bool contextOwnsConnection is true. Since you don't re-use the connection elsewhere, it lets the context manage the connection and Dispose() it when needed.