Area of Triangle Formed by Two Parametric Points and the Focus
For points $$P_1(at_1^2,2at_1)$$ and $$P_2(at_2^2,2at_2)$$:
$$\Delta=\frac a2|t_1-t_2|\left|at_1t_2+a\right|$$
Usage
- Used for area problems involving the focus and two points on the parabola.