**Answer:**

Statement (1) is sufficient.

Statement (2) is not sufficient.

**Step-by-step explanation:**

Consider we need to find check whether the given statements are sufficient or not.

The standard form of a circle is

where, (h,k) is center and r is the radius.

The center of the circle is (0,0). So, the equation of circle is

Statement (1) : The radius of the circle is 4.

**The sum of the squares of the coordinates of P is 16. So statement (1) is sufficient.**

Statement (2) : The sum of the coordinates of P is 0.

We can not solve these two equation because radius is not given.

**Therefore, the statement (2) is not sufficient.**