Question

eliminating the parameter of the parametric equations. aka getting rid of t

x = t^2 + t

y = t^2 - t

Answer 1

Add the two equations to get

x = t^2 + t
y = t^2 - t
-----------
x+y = 2t^2+0t

So we know that


x+y = 2t^2

Answer 2

solve x+y = 2t^2 for t and use this to plug it back into the two original equations (to eliminate t and replace it with an expression in terms of x and y)

Answer 3

But when you solve for t in

x + y = 2t^2

you get t = +sqrt((x+y)/2) & t = -sqrt((x+y)/2)

so which one do we plug in the + or -?

Answer 4

well either one works, so usually the problem adds on something like "t is positive" or "t is nonnegative"

Answer 5

I would go with the positive one since that's usually the one used anyway