Examples from the Web for asymptote
The curve is symmetrical about the axis of y and has the axis of x for its asymptote.
If these factors are all real and distinct, there is an asymptote corresponding to each factor.
But after you have demonstrated to him the properties of the hyperbola and its asymptote, the apparent absurdity vanishes.The Religion of Geology and Its Connected Sciences|Edward Hitchcock
Even so there are asymptote figures in geometry where an infinite length makes only a finite progress in breadth.Theodicy|G. W. Leibniz
The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.