Suppose that $x =\frac { 1 } { t ^ 2 + 1 }$ and $y = t^2$.

1. Express $x$ as a function of $y$.

   Answer (a):

   $x=\frac{1}{y+1}$

2. Express $y$ as a function of $x$.

   Hint (b):

   Solve your equation from part (a) for $y$.

3. How will the graph of the parametric equations given above be different if $x =\frac { 1 } { u + 1 }$ and $y = u$?

   Hint (c):

   What are the possible values of $x$ and $y$ if:

   $x=\frac{1}{t^2+1}\text{ and }y=t^2\text{?}$

   $x=\frac{1}{u+1}\text{ and }y=u\text{?}$