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

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

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

   Hint (b):

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

3. How would the graphs of the parametric equations given above be different if $x = \frac { 1 } { u + 1 }$ and $y = u$ for all real $u$?

   Hint (c):

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