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