The vertices of a triangle are
`[at_(1)t_(2),a(t_(1)+t_(2))],[at_(2)t_(3),a(t_(2)+t_(3))]`
`[at_(3)t_(1),a(t_(3)+t_(1))]`
Find the coordinates of its orthocentre.

Answer

To find the orthocenter of the triangle with vertices given by the coordinates \((at_1t_2, a(t_1 + t_2))\), \((at_2t_3, a(t_2 + t_3))\), and \((at_3t_1, a(t_3 + t_1))\), we will follow these steps:

### Step 1: Identify the vertices of the triangle
Let the vertices of the triangle be:
- \( A = (at_1t_2, a(t_1 + t_2)) \)
- \( B = (at_2t_3, a(t_2 + t_3)) \)
- \( C = (at_3t_1, a(t_3 + t_1)) \)