Asymptote is a line of a graph that does not intersect. The distance between the asymptote and curve approaches zero when they head towards infinity. There are three kinds of asymptotes i.e., oblique, horizontal and vertical asymptotes. This online Asymptote Calculator finds both horizontal and vertical asymptotes. When you plug in the function in the calculator, it will find both the asymptotes and plot graph.

Follow these three cases :

Follow these three cases :

- If the degree of the numerator is greater than the degree of denominator, then there are no horizontal asymptote.
- If the degree of the numerator is less than the degree of denominator, then y = 0 is the horizontal asymptote.
- If the degree of the numerator is equal to the degree of denominator, then the rational has non-zero horizontal asymptote.

To find vertical asymptote :

Set the value of denominator as zero and solve for x to get the vertical asymptote.

Below problems are based on asymptote .

### Solved Examples

**Question 1:**Find the horizontal and vertical asymptotes of y = $\frac{x^2+6x+1}{2x^2-8}$ ?

**Solution:**

For horizontal asymptote :

Here, the degree is 2.

Dividing the terms, we get

y = $\frac{x^2}{2x^2}$

y = $\frac{1}{2}$

For vertical asymptote :

$2x^2$ - 8 = 0

$2x^2$ = 8

$x^2$ = $\frac{8}{2}$

$x^2$ = $\pm$ 4

Answer : Horizontal asymptote : y = $\frac{1}{2}$

Vertical asymptote : $x^2$ = $\pm$ 4

**Question 2:**

Find the horizontal and vertical asymptotes of y = $\frac{x+3}{x^2+9}$ ?

**Solution:**

For horizontal asymptote :

Here, the degree of denominator is greater than numerator, y values is dragged to x axis. Therefore, the horizontal asymptote is y = 0.

For vertical asymptote :

$x^2+9$ = 0

$x^2$ = -9

Since the number is negative, there are no vertical asymptotes.

Answer : Horizontal asymptote : y = 0

Vertical asymptote : none