# Asymptote Formula

An asymptote is a straight line with respect to a curve such that it tends to meet the curve at infinity. This can be more clearly understood as a line drawn at a minimum parallel distance to the tangent of a curve, such that it does not cut or touch the curve. Asymptote formula is generally defined, for a hyperbola. Asymptote Formula is represented as an equation of a line.

## What is an Asymptote Formula?

The asymptotes of a hyperbola are a pair of straight lines. The asymptotes of a hyperbola having an equation x^{2}/a^{2} - y^{2}/b^{2} = 0 is given by the following formula:

Equation of Asymptotes: y = b/a.x, and y = -b/a.x

Equation of Pair of Asymptotes: x^{2}/a^{2 } - y^{2}/b^{2} = 0

Let us check out a few solved examples to more clearly understand Asymptotes Formula.

## Examples Using Asymptote Formula

**Example 1: **Find the equation of pair of asymptotes of a hyperbola x^{2}/16 - y^{2}/25 = 1.

**Solution:**

Given equation of the hyperbola is x^{2}/16 - y^{2}/25 = 1

For a hyperbola having an equation x^{2}/a^{2} - y^{2}/b^{2} = 1 the equation of its pair of asymptotes is bx/a and -bx/a

Here it is known that a = 4 and b = 5

Hence the equation of pair of asymptotes is y = 4x/5 and y =-4x/5

**Answer:** Equation of the pair of aymptotes is 5y-4x = 0 and 5y +4x =0

**Example 2: **Find the equations of the asymptotes of the hyperbola x^{2}/49 - y^{2}/36 = 1.

**Solution:**

The given equation of the hyperbola is x^{2}/49 - y^{2}/36 = 1

x^{2}/7^{2} - y^{2}/6^{2} = 1

Let us compare the above equation with the standard equation of a hyperbola x^{2}/a^{2} - y^{2}/b^{2} = 1

We get a = 7 and b = 6

Further the equations of the asymptotes is y = b/a.x, and y = -b/a.x

y = 6x/7 and y = -6x/7

7y = 6x and 7y = -6x

7y- 6x = 0 and 6x + 7y = 0

**Answer:** Hence the equations of the asymptotes are 7y- 6x = 0 and 6x + 7y = 0