Hi guys, I was trying to sketch a polar curve but my curve was different from the curve on maple(I plotted the same curve on maple). 1. The problem statement, all variables and given/known data Here is the whole question, I am using t as theta. The hyperbolic spiral is described by the equation rt=a whenever t>0,where a is a positive constant. Using the fact that lim(t->0)sint/t=1,show that the line y=a is a horizontal asymtote to the spiral. Sketch the spiral. 2. Relevant equations 3. The attempt at a solution Since y=rsint, substituting r=y/sint into rt=a we get y=asint/t. By taking the limit of both sides as t->0 we get y=a. The thing I don't understand is, why is y=a a horizontal asymptote on the polar coordinates? Isn't y=a only an asymptote on the cartesian coordinates of the curve rt=a(when you convert it in terms of x and y)? Ok so I plotted the polar curve. The difference between my curve and the one on maple is the behavior of the curve as t tends to 0. My curve is a bit like y=1/x as x tends to +infinity(I am talking about the SHAPE of my polar curve as t tends to 0). After that it is just like a spiral as t increases. However, the one shown on maple tends to y=a as t tends to 0(as in, it tends to a horizontal line y=a but my curve tends to the x-axis like y=1/x). Obviously, both curves (mine and maple's) obey the fact that r tends to infinity as t tends to 0(because rt=a so r=a/t). But why the horizontal asymptote? Am I missing something in here? Any help would be appreciated.