Parametric Parabola

You need to show that T and U have the same y coordinate.

T has y coordinate apq
U has y coordinate -apr

but if you look at the coordinates of P and Q and note that PQ is perpendicular to the axis of the parabola then it should be clear that q = -r

so both T and U have y coordinates apq and thus TU is horizontal and thus perpendicular to the vertical parabola axis.

Rom:

You need to show that T and U have the same y coordinate.

T has y coordinate apq
U has y coordinate -apr

but if you look at the coordinates of P and Q and note that PQ is perpendicular to the axis of the parabola then it should be clear that q = -r

so both T and U have y coordinates apq and thus TU is horizontal and thus perpendicular to the vertical parabola axis.

Of course, thanks Rom, much appreciated.