ABCTE Secondary Math Practice Exam 2025 – The Complete All-in-One Guide for Exam Success

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\