The new curve contains all of the information about the original curve’s tangent lines. For example, it crosses the y-axis whenever the original curve has a horizontal tangent line. The straight line y = mx + b, or (x(t), y(t)) = (t,mt + b), has only one tangent line and thus a trivial transformation to a point, (x∗(t), y∗(t)) = (m, b). Some conic sections transform to conic sections. For examp...