Question 1137322
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x = t^2 + 1

y = t^2 - 1.


Subtract the second equation from the first. You will get


x - y = 1 - (-1) = 2.


So, you eliminated the variable " t " and obtained the equation of the straight line x - y = 2 in (x,y)- coordinate plane.


The image of the map x ----> (t^2+1,t^2-1) is the ray: half of the straight line in (x,y)-coordinate plane.
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Explained, solved and completed.