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

The standard equation of a circle is given by :

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,

Simplifying,

Answer is option first:

x² + y² =r²

-2 is the right