Let P be the point (at2, 2at1), and Q be the point (at22, 2at2), so that T is the point {at1t2, a(t1 + t2)}.
The perpendicular, TU, from T on this straight line
Similarly TU' has the same numerical value.
The angles PST and QST are therefore equal.
and the angles TSP and TSQ are equal, the triangles SPT and STQ are similar, so that