Given the implicit equation of a Conic $C$, how to determine its parametric representation? I went thought this report and it has an algorithm:
- Fix a point $p$ on the conic. Consider the pencil of lines through $p$. Formulate the line equations.
- Substitute for $y$ in the conic equation, solve for $x(t)$.
- Use the fine equations to determine $y(t)$.
The algorithm described requires determining a point on the conic. Is there an algorithm to determine a rational point on a conic?