Singular point of a curve

A singular point of a curve refers to a point on the curve where the curve fails to be well-behaved in some way. Specifically, a singular point is typically where the curve does not have a well-defined tangent, which can occur for a variety of reasons. The most common forms of singular points include: 1. **Cusp**: A point where the curve meets itself but does not have a unique tangent direction. There might be a sharp turn at the cusp.