how do you eliminate the parameters for x=1-t^2 and y=1+t?
t^2 = 1-x
t = y-1 so t^2 = y^2-2y+1
so
y^2-2y+1 = 1 - x
so its y^2-2y=x
not solving for y?
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 :)
find directrix of 1/1-cos theta
To eliminate the parameters for x=1-t^2 and y=1+t, we can substitute the value of t from one equation into the other equation.
Let's start by substituting the value of t from the equation y=1+t into the equation x=1-t^2.
Since y=1+t, we can rewrite the equation x=1-t^2 as x=1-(y-1)^2.
Now, let's expand and simplify the equation x=1-(y-1)^2:
x=1-(y-1)^2
x=1-(y^2-2y+1)
x=1-y^2+2y-1
x=-y^2+2y
So, we have eliminated the parameter t and obtained the equation x=-y^2+2y.