Question

Which is the standard equation for a circle centered at the origin with radius r?

A. x2 + y2 = r
B. x2 = y2 + r2
C. x + y = r
D. x2 + y2 = r2

Answer 1

D. This is the base equation. 

Answer 2

The standard equation of a circle is given by :

$(x-h)^{2} + (y-k)^{2} =r^{2}$

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

Now in the question we are given that the center is at origin.

So coordinate of center becomes (h,k) =(0,0)

radius is r.

So plugging these values in the standard equation, we get,

$(x-0)^{2} + (y-0)^{2} =r^{2}$

Simplifying,

$(x)^{2} + (y)^{2} =r^{2}$

Answer is option first:

x² + y² =r²