What is the equation of the unit circle?

The equation of the unit circle is defined as the set of all points ((x, y)) that are at a distance of 1 unit from the origin ((0, 0)) in a Cartesian coordinate system. This relationship is captured mathematically through the equation (x^2 + y^2 = r^2), where (r) represents the radius of the circle.

For the unit circle specifically, the radius (r) is 1. Therefore, we substitute (r) with 1 in the general equation, resulting in (x^2 + y^2 = 1). This equation indicates that for any point on the unit circle, the sum of the squares of the x-coordinate and the y-coordinate will always equal 1, maintaining the circle's definition.

The choice that states (x^2 + y^2 = 1) is the correct representation of the unit circle because it accurately describes this geometric figure. The other choices either misrepresent the relationship or describe different figures entirely. For instance, (x^2 + y^2 = 0) describes a single point at the origin, (x^2 - y^2 = 1\