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I am asked to show that the line ##x+y+a=0## is an asymptote. So, I have to prove that when ##t \to \infty##, the curve tends to that line. My doubt is: The limit of ##\alpha(t)## when ##t \to \infty## is ##(0,0)##, how is it possible that the curve tends to the origin and at the same time to that line? How could I show that the line is in fact an asymptote of the curve?