Tricky Parametric equation

  • #1
I would like to convert these parametric equations into a single
f(x,y) = 0 function.

X(t) = t^2 + t + 1
Y(t) = t^2 - t +1

In fact, what stops me is the imaginary roots of the parametric polynomials.

Is there a way to get around the seemingly impossible explicit solving of the quadratics to isolate either X or Y ?
 

Answers and Replies

  • #2
0rthodontist
Science Advisor
1,230
0
Note that x - t = y + t (or just subtract y(t) from x(t)).
 
Last edited:
  • #3
1,074
1
Gagle The Terrible said:
I would like to convert these parametric equations into a single
f(x,y) = 0 function.

X(t) = t^2 + t + 1
Y(t) = t^2 - t +1

In fact, what stops me is the imaginary roots of the parametric polynomials.

Is there a way to get around the seemingly impossible explicit solving of the quadratics to isolate either X or Y ?
First note that X - Y = 2t, but also notice that these are both quadratic equations so you can solve one of them or the other to find t in terms of X or Y and then substitute this into X - Y = 2t or the equation for the other variable.
 
  • #4
0rthodontist
Science Advisor
1,230
0
You just want to substitute t = (x - y) / 2. There's no need to solve any quadratics.
 
  • #5
1,074
1
0rthodontist said:
You just want to substitute t = (x - y) / 2. There's no need to solve any quadratics.
Darn, I guess I should have seen that since I did notice that x - y = 2t.
 

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