# Hyperbola Center, Axis, Eccentricity & Asymptotes Calculator

getcalc.com's **Hyperbola Formulas & Calculator** is an online basic geometry tool to calculate center, axis, eccentricity & asymptotes of hyperbola shape or plane, in both US customary & metric (SI) units.

## Steps to Find Center, Axis, Eccentricity & Asymptotes of a Hyperbola

The step by step workout for how to find what is the center, axis, eccentricity & asymptotes of a hyperbola.__workout :__

step 1 Address the formula input parameter and values

x_{0} = 5

y_{0} = 4

a = 5

b = 4

step 2 Apply x, y, a & b values in F (x, y) formula

F(x, y) = (x_{0} + √a² + b² , y_{0})

= (5 + √5² + 4² , 4)

= (5 + √25 + 16 , 4)

= (5 + √41 , 4)

= (5 + 6.4031 , 4)

F(x, y)= 11.4031, 4

step 3 Apply x, y, a and b values in F’ (x, y)

F’ (x, y) = (x_{0} - √a² + b² , y_{0})

= (5 - √5² + 4² , 4)

= (5 - √25 + 16 , 4)

= (5 - √41 , 4)

= (5 - 6.4031 , 4)

F’ (x, y)= -1.4031, 4

step 4 Apply a and b values in eccentricity formula

Eccentricity = √a² + b²

= √5² + 4²

= √41

Eccentricity = 6.4031

step 5 Apply the values a, b, x_{0}, y_{0} in asymptotes H’L formula

Asymptotes H’L = b/ax + (y_{0} - b/ax_{0})

= 4/5x + (4 - 4/55)

= 0.8x + (4 - (0.8 x 5))

= 0.8x + (4 - (4))

Asymptotes H’L = 0.8x + 0

step 6 Apply the values a, b, x_{0}, y_{0} in asymptotes L’H formula

Asymptotes L’H = -b/ax + (y_{0} + b/ax_{0})

= 4/5x + (4 + 4/55)

= -0.8x + (4 - (-0.8 x 5))

= -0.8x + (4 - (-4))

Asymptotes L’H = -0.8x + 8

## Definition & Formulas

**Hyperbola** is a geometric shape represents the open curve with two symmetrical intersection of cone having same vertexes pointing each other on the same axis.