Bad luck :( Next you you'll win.
I showed up to the roundhouse at ~5:30 but I didn't recognise anyone/ no one called out to me, so I left and ended up drink with friends :p
$Using $ x+t^2y=2ct, $ we have the tangent at $ P $ having eqn $ x+t_1^2y=2ct_1 $ and similarly tangent at T has eqn $ x+t_2^2y=2ct_2. \\ $Now find where they intersect$.$