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} = 1 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} = 1
Let us check out a few solved examples to more clearly understand Asymptotes Formula.
Solved Examples on 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 x^{2}/a^{2}  y^{2}/b^{2} = 0.
Hence the equation of pair of asymptotes is x^{2}/16  y^{2}/25 = 0.
Answer: Equation of parir of aymptotes is x^{2}/16  y^{2}/25 = 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
6x  7y = 0 and 6x + 7y = 0
Answer: Hence the equations of the asymptotes are 6x  7y = 0 and 6x + 7y = 0