Parametric equations of Parabola

[Ice-cream]

this is a Q i'm having trouble with...can some1 help me out?

PT is the tangent at P, a variable point on the parabola xsquared = -16y. If T lies on the directrix, find the locus of the midpoint PT.

what i've already gathered is that the directrix must be y=4. I'm not sure if P's coordinate is (-4tsquared, 8t) because the parabola isn't in the form ysquared = 4ax but for the coordinate of T, all i know is that its y value must be 4. Can any1 tell me wat im missing?

[Crash]

Y= at^2

or Y= 2at are others you could try, see if they work

[Dapthar]

PT is the tangent at P' date=' a variable point on the parabola xsquared = -16y. If T lies on the directrix, find the locus of the midpoint PT.

what i've already gathered is that the directrix must be y=4. I'm not sure if P's coordinate is (-4tsquared, 8t) because the parabola isn't in the form ysquared = 4ax but for the coordinate of T, all i know is that its y value must be 4. Can any1 tell me wat im missing?[/quote']You're a bit off there.

[math]x^2=-16y[/math]

[math]\iff \frac{-x^2}{16}=y[/math]

Setting [math]x=t[/math], we get the following:

[math](t, \frac{-t^2}{16})[/math]