Vector Equations of Curves

Vector equations of curves is part of the Vectors topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-02). This subtopic treats a pair (or triple) of parametric equations as one vector equation, such as \(\mathbf{r} = \begin{pmatrix} x(t) \\ y(t) \end{pmatrix}\) with parameter \(t\), describing curves in two and three dimensions.

Students and teachers will cover how to recognise circles, parabolas, ellipses and hyperbolas from their vector form, write a vector equation for a given graph, and eliminate the parameter to find the Cartesian equation — linking parametric and Cartesian descriptions in the HSC Extension 2 course.