A straight line L is called an asymptotes of an infinite branches of a curve if the perpendicular distance of a point P on that branch from the straight line L tend to zero as P moves to infinity along the branch.

An asymptote of a curve is a line to which the curve converge. In other words, the curve and its asymptotes get infinity close but they never meet. They are use in graphing rational equation.





In most cases, the asymptotes of a curve can be found by taking the limit of a value where the function is not defined. Typical examples would be

and

or the point where the denominator of a rational function equals zero. Asymptotes are broadly classified into three categories

1. Horizontal asymptote

2. Vertical asymptote

3. Oblique asymptote





1. Horizontal asymptote

2. Vertical asymptote

3. Oblique asymptote

☆Rule to find asymptotes parallel to x-axis

☆Rule to find asymptotes parallel to y-axis

Example

Horizontal asymptote is a line which is parallel to x-axis. When x goes to infinity then curve approaches some constant value.Vertical asymptote is a line which is parallel to y-axis. When x goes to infinity then curve approaches some constant value.An asymptote, which is neither parallel to x-axis nor y-axis is called an oblique asymptote. When x goes to infinity then curve goes toward a line y=mx+c.Equate to zero the real linear factor in the coefficient of higher power of x in the equation of the given curve.It should be noted properly that if coefficient of higher power of x in the equation of the given curve is a constant or has no real linear factor, then the curve has no asymptote parallel to x-axis.Equate to zero the real linear factor in the coefficient of higher power of y in the equation of the given curve.It should be noted properly that if coefficient of higher power of y in the equation of the given curve is a constant or has no real linear factor, then the curve has no asymptote parallel to y-axis.Find the vertical and horizontal asymptotes of the curve The equation of the given curve is (1)The coefficient of highest power of x in (1) is