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?
Answers
The questions is incomplete here is the complete 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
The coordinates of P are (x,y), then the question asks about the value of x^2 + y^2.
The circle with center (a, b) and radius r is the set of all points (x, y) such that:
(x−a)2+(y−b)2=r2
The radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b.
If the circle is centered at the origin (0, 0), then the equation simplifies to:
x^2+y^2=r^2
The first statement of the question gives the direct answer: x^2 + y^2 = r^2 = 4^2.
The second statement is not sufficient.