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**THSKluv** Eliminate the parameter, t to obtain the cartesian equation in x and y. Sketch the curve, taking note of any restrictions

d) $\displaystyle x = t + \frac{1}{t}, ~ y = t^2 - \frac{1}{t^2}$

e) $\displaystyle x = t + \frac{1}{t}, ~ y= t - \frac{1}{t}$

f) $\displaystyle x = \frac{1 - t^2}{1 + t^2}, ~ y = \frac{2t}{1+t^2}$

I know it's a lot and i really dont expect this all to be answered, i just put all the questions which i had serious trouble with and i would be SO grateful to anyone who could give me a few pointers on how to solve these because i just dont know how to get rid of the t OR find the restrictions. again , i know there are alot of questions and im not just expecting answers or a cheap way to get answers for hw, i realli just dont understand it and would seriously appreciate any help .

thankyou guyz !