Hyperbola Formula
Before learning the hyperbola formula, let us recall what is a hyperbola. Hyperbola is an open curve that has two branches which look mirror image of each other. For any point on any of the branches, the absolute difference between the point from foci is constant and equals to 2a, where a is the distance of the branch from the center. The Hyperbola formula helps us to find various aspects and related quantities of the hyperbola. Various hyperbola formulas are explained below.
What Are the Hyperbola Formulas?
There are different aspects related to hyperbola formulas such as the equation of hyperbola, the major and minor axis, eccentricity, asymptotes, vertex, foci, and semilatus rectum. Let us learn each of them.

Equation of hyperbola
(x  \(x_0\))^{2} / a^{2}  ( y  \(y_0\))^{2} / b^{2} = 1 
The major and minor axis
y = y_{0} is the major axis, and its length is 2a, whereas x = x_{0} is the minor axis, and its length is 2b 
Eccentricity(e)
e = \(\sqrt {1 + \dfrac {b^2}{a^2}}\) 
Asymptotes
y = y_{0 }− (b / a)x + (b / a)x_{0}
y = y_{0 }+ (b / a)x  (b / a)x_{0} 
Vertex
(a, y_{0}) and (−a, y_{0}) 
Focus (foci)
(x_{0 }+ \(\sqrt{a^2+b^2} \),y_{0}), and (x_{0 } \(\sqrt{a^2+b^2} \),y_{0}) 
Semilatus rectum(p)
p = b^{2} / a
Where,
 x_{0},y_{0} are the center points.
 a = semimajor axis.
 b = semiminor axis.
Let us see the applications of hyperbola formulas in the following solved examples.
Solved Examples Using hyperbola Formula

Example 1: The equation of the hyperbola is given as (x−5)^{2}/4^{2}−(y−2)^{2}/ 6^{2} = 1. Use the hyperbola formulas to find the length of the Major Axis and Minor Axis.
Solution:
Using the hyperbola formula for the length of the major and minor axis
Length of major axis = 2a, and length of minor axis = 2b
Length of major axis = 2×4 = 8, and Length of minor axis = 2×6 = 12
Answer: The length of the major axis is 8 units, and the length of the minor axis is 12 units.

Example 2: The equation of the hyperbola is given as (x−5)^{2}/4^{2}−(y−2)^{2}/ 6^{2} = 1. Find the asymptote of this hyperbola.
Solution:
Using the one of the hyperbola formulas (for finding asymptotes):
y = y_{0 }− (b / a)x + (b / a)x_{0} and y = y_{0 }− (b / a)x + (b / a)x_{0}y = 2  ( 6/4)x + (6/4)5 and y = 2 + ( 6/4)x  (6/4)5
Answer: Asymptotes are y = 2  ( 3/2)x + (3/2)5, and y = 2 + ( 3/2)x  (3/2)5.