Parametrics Help! (1 Viewer)

[foram]

I need help with this question please. I'm not sure what i'm doing wrong??

The straight line drawn from point P of a parabola to the vertex cuts the directrix at T. Prove that if the focus is S that ST is parallel to the tangent at P.

 

[namburger]

Your co-ordinates of T are wrong.
To find T:
The equation of OP is y = (at^2/2at)x
Which can be simplfied to y=tx/2
Let y = -a, x=-2a/t
Co-ordinates of T is (-2a/t,-a)

Find the gradient of ST:
T (-2a/t,-a) & S(0,a)
m of TS = t which is parralel to the tangent at P(2at,at^2)

 

[foram]

thankyou