Area of Triangle Formed by Two Parametric Points and the Focus

Rarely Tested

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.

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