The curve is symmetrical about the axis of y and has the axis of x for its asymptote.
But after you have demonstrated to him the properties of the hyperbola and its asymptote, the apparent absurdity vanishes.
Even so there are asymptote figures in geometry where an infinite length makes only a finite progress in breadth.
If these factors are all real and distinct, there is an asymptote corresponding to each factor.
The area of the loop, which equals the area between the curve and its asymptote, is 3a/2.
asymptote, a line always approaching some curve but never meeting it.
"straight line continually approaching but never meeting a curve," 1650s, from Greek asymptotos "not falling together," from a- "not" + syn "with" + ptotos "fallen," verbal adjective from piptein "to fall" (see symptom). Related: Asymptotic.