\( x ^ { 2 } + y ^ { 2 } - 1 \)

The equation \( x^2 + y^2 - 1 = 0 \) describes a circle with a radius of 1 centered at the origin (0,0) in a Cartesian coordinate system. This is a foundational concept in geometry that serves as a building block for understanding more complex shapes and relationships in mathematics. In practical terms, this equation is often used in fields such as physics and engineering, where circular motion is involved or when designing mechanisms that involve rotation. For example, you might find it relevant in robotics for path planning or in animations where circular paths are needed, making it highly applicable in real-world scenarios.