Relation between conic and dual conic

When ${\tt m}$ varies along the conic, it satisfies ${\tt m}^\top {\bf C} {\tt m}$ and thus the tangent line ${\tt l}$ to the conic at ${\tt m}$ satisfies ${\tt l}^\top {\bf C}^{-1} {\tt l} = 0$. This shows that the tangents to a conic ${\bf C}$ are belonging to a dual conic ${\bf C}^* \sim {\bf C}^{-1}$ (assuming ${\bf C}$ is of full rank).