The aim of this chapter is to study the shape of a *plane curve y*=*f*(*x*). For this purpose, we must investigate the variation of the function *f*, in the case of unlimited increase and absolute value and of *x* or *y*, or both, of a variable point (*x*, *y*) on the curve. The study of such variation of the function requires the concept of an asymptote. Before defining an asymptote to a curve, let us define finite and infinite branches of a plane curve as follows:

Consider the equation of the ellipse Solving this equation, we get

The first equation represents the upper half of the ellipse while the second equation represents ...

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