Solve Parametric Equations & Sketch Curve

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Homework Statement


how can we eliminate the parameter of these functions:
x= t-2
y= t^2 +1
and sketch its curve

Homework Equations





The Attempt at a Solution



I can't find the relations between these 2 functions
 
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They are related through t.
 
But how can I eliminate t and make a function of x and y?
 
You could start by expressing t in terms of x.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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