Asymptote Formula

About Asymptote Formula

A straight line w.r.t a curve that tends to meet the curve at infinity is called an asymptote. A line drawn at a minimum parallel distance to the tangent of a curve that does not cut or touch the curve can be more readily comprehended. For a hyperbola, the asymptote formula is commonly defined. The Asymptote Formula is written as a line equation.

What is an Asymptote Formula?

A hyperbola's asymptote is a pair of straight lines. A hyperbola's asymptotes using an equation x2/a2 - y2/b2 = 0 is given by the following formula:

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

Pair of Asymptotes equation: x2/a2 - y2/b2 = 0

Exercising the Asymptote Formula

Example 1: : Find the equation for a pair of hyperbola asymptotes. x2/16 - y2/25 = 1.

Solution:

Hyperbola given equation is x2/16 - y2/25 = 1

An equation is needed for a hyperbola x2/a2 - y2/b2 = 1

Its pair of asymptotes equation is bx/a, -bx/a

Here we know that a = 4 and b = 5

Thus, equation of pair of asymptotes are y = 4x/5 and y =-4x/5

Example 2: Find the equations of asymptotes of hyperbola given as: x2/49 - y2/36 = 1.

Solution:

The given equation of the hyperbola is x2/49 - y2/36 = 1

this emply: x2/72 - y2/62 = 1

Now compare the above equation with the standard equation of a hyperbola x2/a2 - y2/b2 = 1

We have 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

Thus, the equations of the asymptotes are 7y- 6x = 0 and 6x + 7y = 0

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