- A point is a degenerate case of a circle, namely one with radius 0. The circle is a degenerate form of an ellipse, namely one with eccentricity 0.
- The line is a degenerate form of a parabola if the parabola resides on a tangent plane.
- A hyperbola can degenerate into two lines crossing at a point, through a family of hyperbolas having those lines as common asymptotes.
- See "General position" for other examples.