Question

A certain circle in the xy-plane has its center at the origin. If P is a point on the circle, what is the sum of the squares of the coordinates of P ? (1) The radius of the circle is 4.(2) The sum of the coordinates of P is 0.

Answer 1

Statement (1) is sufficient.

Statement (2) is not sufficient.

Explanation:

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

The standard form of a circle is

`(x-h)^2+(y-k)^2=r^2`

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

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

`(x-0)^2+(y-0)^2=r^2`

`x^2+y^2=r^2`

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

`x^2+y^2=(4)^2`

`x^2+y^2=16`

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.

`x^2+y^2=r^2`

`x+y=0`

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

Therefore, the statement (2) is not sufficient.