Properties of a circle please help me

Question

Explain how you know that the origin is the centre of a circle represented by x2 + y2 =41

Answer 1

Definition of a circle is the set of points that are the SAME distance from the center

So for the center at (A,B) we have ANY point on the circle (x,y) such that

sqrt((x-A)^2 + (y-B)^2 )= r <---- Distance formula

squaring both sides:

(x-A)^2 + (y-B)^2 = r^2

This is the equation of the circle...

Now for center at the origin as you said, we have A=0 and B=0

which makes the equation

x^2 +y^2 = r^2

<end of proof>