Answer :
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
[tex](x-h)^2+(y-k)^2=r^2[/tex]
where, (h,k) is center and r is the radius.
The center of the circle is (0,0). So, the equation of circle is
[tex](x-0)^2+(y-0)^2=r^2[/tex]
[tex]x^2+y^2=r^2[/tex]
Statement (1) : The radius of the circle is 4.
[tex]x^2+y^2=(4)^2[/tex]
[tex]x^2+y^2=16[/tex]
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.
[tex]x^2+y^2=r^2[/tex]
[tex]x+y=0[/tex]
We can not solve these two equation because radius is not given.
Therefore, the statement (2) is not sufficient.