SOLUTION: Name the curve and find the rectangular form for the parametric equations.? The equations are: x(t)= 1/√t+1 and y(t)=t/t+1 t ≠ -1

Algebra ->  Vectors -> SOLUTION: Name the curve and find the rectangular form for the parametric equations.? The equations are: x(t)= 1/√t+1 and y(t)=t/t+1 t ≠ -1      Log On


   

Question 1173368: Name the curve and find the rectangular form for the parametric equations.?
The equations are:
x(t)= 1/√t+1 and y(t)=t/t+1
t ≠ -1
Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.

From  x = 1%2Fsqrt%28t%2B1%29,  you get, squaring,


    x^2 = 1%2F%28t%2B1%29,

    x^2*(t+1) = 1

    x^2*t + x^2 = 1

    x^2*t = 1 - x^2

    t = %281-x%5E2%29%2Fx%5E2.


Now substitute it into the expression for y = t%2F%28t%2B1%29.  You will get


    y = %281-x%5E2%29%2Fx%5E2%29 : %28%281-x%5E2%29%2Fx%5E2+%2B+1%29 = %281-x%5E2%29%2Fx%5E2%29 : 1%2Fx%5E2 = 1- x^2.


So, the curve is the parabola


    y = 1- x^2.      ANSWER

Solved.



Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi
x(t)= 1/√t+1 and y(t)=t/t+1 t ≠ -1
x^2 = 1/(t+1)  0r (t+1) = 1/x^2   0r t = 1/x^2 -1
substitute 
y=t%2F%28t%2B1%29+=+%28%281%2Fx%5E2%29-1%29%2F+%281%2Fx%5E2%29+=+1+-+x%5E2
  Wish You the Best in your Studies.