10. Prove that the area of the triangle whose vertices are : (a * t_{1} ^ 2, 2a*t_{1}); (a * t_{2} ^ 2, 2a*t_{2}); (a * t_{3} ^ 2, 2a*t_{3}) is a ^ 2 * (t_{1} - t_{2})(t_{2} - t_{3})(t_{3} - t_{1})
To prove the area of the triangle with vertices \( (a \cdot t_1^2, 2a \cdot t_1), (a \cdot t_2^2, 2a \cdot t_2), (a \cdot t_3^2, 2a \cdot t_3) \) is \( a^2 \cdot (t_1 - t_2)(t_2 - t_3)(t_3 - t_1) \), we can use the formula for the area of a triangle formed by three points in a coordinate plane.
The formula for the area of a triangle with vertices \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) is given by:
Therefore, we have proved that the area of the triangle with vertices \( (a \cdot t_1^2, 2a \cdot t_1), (a \cdot t_2^2, 2a \cdot t_2), (a \cdot t_3^2, 2a \cdot t_3) \) is \( a^2 \cdot (t_1 - t_2)(t_2 - t_3)(t_3 - t_1) \).
