\( ( x - 2 ) ^ { 2 } + ( 2 y + 5 ) ^ { 2 } = 0 \)

This equation can only hold true when both components equal zero. For \( ( x - 2 ) ^ { 2 } = 0 \), we find \( x = 2 \). Then for \( ( 2 y + 5 ) ^ { 2 } = 0 \), we solve for \( y \) to get \( y = -\frac{5}{2} \). So, the only solution is the point \( (2, -\frac{5}{2}) \), making it a single point in the Cartesian plane. This equation represents a specific case where we're looking at a circle that has degenerated into a single point. In real-world applications, this might represent a position where two variables must meet certain criteria, such as in a coordinate system for an engineering project or in optimization scenarios where only one optimal solution exists.