Final answer:
The correct equation for a circle with the center at (0,0) and a radius of 1 is (x)^2 + (y)^2 = 1. This comes from the standard form of a circle's equation, which is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center and r is the radius.
Step-by-step explanation:
The question asks to write the equation of a circle with the center at (0,0) and a radius of 1. In standard form, the equation of a circle with center (h,k) and radius r is given as (x-h)^2 + (y-k)^2 = r^2. For a circle centered at the origin (0,0), h and k would both be 0, and since the radius is given as 1, r would be 1, which gives us r^2 as 1. Therefore, the equation of the circle is (x-0)^2 + (y-0)^2 = 1.
Looking at the options provided:
- (a) (x+0)^2 + (y)^2 = -1 is incorrect because the radius squared cannot be negative.
- (b) (x+0)^2 + (y+0)^2 = 4 is incorrect because the radius squared should be 1, not 4.
- (c) (x+0)^2 + (y)^2 = 2 is incorrect as the radius squared should be 1.
- (d) (x)^2 + (y)^2 = 1 is the correct equation, as it simplifies to the right form of the equation for a circle centered at the origin with a radius of 1.