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 x2/a2 - y2/b2 = 0 is given by the following formula:
Equation of Asymptotes: y = b/a.x, and y = -b/a.x
Equation of Pair of Asymptotes: x2/a2 - y2/b2 = 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 x2/16 - y2/25 = 1.
Given equation of the hyperbola is x2/16 - y2/25 = 1
For a hyperbola having an equation x2/a2 - y2/b2 = 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 x2/49 - y2/36 = 1.
The given equation of the hyperbola is x2/49 - y2/36 = 1
x2/72 - y2/62 = 1
Let us compare the above equation with the standard equation of a hyperbola x2/a2 - y2/b2 = 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