how do you eliminate the parameters for x=1-t^2 and y=1+t?

Answer 1

t^2 = 1-x

t = y-1 so t^2 = y^2-2y+1
so
y^2-2y+1 = 1 - x

Answer 2

so its y^2-2y=x

not solving for y?

Answer 3

y^2 - 2 y = -x

You were asked to eliminate the parameter t, not to solve for y. However I do not know the traditions of your particular group :)

Answer 4

find directrix of 1/1-cos theta