I have an upcoming exam, and I'm having trouble grasping some concepts. The things that are currently perplexing me are parametric equations and rectangular equations and converting between the two. I have a problem like this Given the parametric equations x = e^(-t) + 1 and y = e^(-2t) - 3, find the corresponding rectangular equation and sketch the curve of orientation. To eliminate the parameter, I set the x equation equal to t as such: t = -ln(x-1) and then substituted this value into the y equation to get: y = e^[ln(x - 1)] - 3 and got y = x - 4 as my final equation, but I'm not so confident in this answer. Then I'm told to find a set of parametric equatiions for the rectangular equation (x - 2)² + y² = 9 I set x equal to t and soved for y and ended up with y = sqrt(t²-4t+13) This seems like only half the answer to me, but I barely know where to start, let alone how to continue. I'm sure I'll be kicking myself when I finally figure these concepts out, but I can't for the life of me wrap my head around any of it, and I have no access to a tutor between now and my exam. Any help/guidance is appreciated. Edit: I see now I may have posted this in the wrong forum. My bad.