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Hyperbola Calculator

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Given the hyperbola below

calculate the equation of the asymptotes

intercepts, foci points

eccentricity and other items.


Determine transverse axis:

Since our first variable is y

the hyperbola has a vertical transverse axis

Determine the equation of the asymptotes:

a = √256

a = 16

b = √25

b = 5

Calculate asymptote 1:
Asymptote 1  =  ax
  b

Asymptote 1  =  16x
  5

Calculate asymptote 2:
Asymptote 2  =  -ax
  b

Asymptote 2  =  -16x
  5

Determine y-intercepts:

y-intercepts = ±a

y-intercepts = ±16

y-intercepts =(0, 16) and (0, -16)

Determine the foci:

Our foci are at (0,c) and (0,-c) where

a2 + b2 = c2

Therefore, c = √a2 + b2

a = √162 + 52

c = √256 + 25

c = √281

c = 16.76305461424

Foci = (0,16.76305461424) and (0,-16.76305461424)

Calculate eccentricity ε
ε  =  c
  a

ε  =  16.76305461424
  16

ε = 1.04769091339

Calculate latus rectum:
Latus Rectum  =  2b2
  a

Latus Rectum  =  2(5)2
  16

Latus Rectum  =  2(25)
  16

Latus Rectum  =  50
  16

Latus Rectum = 3.125

Calculate semi-latus rectum l:
l  =  Latus Rectum
  2

l  =  3.125
  2

l = 1.5625

Final Answers:

hyperbola has a vertical
y-intercepts = (0, 16) and (0, -16)
Foci = (0,16.76305461424) and (0,-16.76305461424)
ε = 1.04769091339
Latus Rectum = 3.125
l = 1.5625

You have 1 free calculations remaining


What is the Answer?

hyperbola has a vertical
y-intercepts = (0, 16) and (0, -16)
Foci = (0,16.76305461424) and (0,-16.76305461424)
ε = 1.04769091339
Latus Rectum = 3.125
l = 1.5625

How does the Hyperbola Calculator work?

Free Hyperbola Calculator - Given a hyperbola equation, this calculates:
* Equation of the asymptotes
* Intercepts
* Foci (focus) points
* Eccentricity ε
* Latus Rectum
* semi-latus rectum
This calculator has 1 input.

What 2 formulas are used for the Hyperbola Calculator?

standard form of a hyperbola that opens sideways is (x - h)2 / a2 - (y - k)2 / b2 = 1
standard form of a hyperbola that opens up and down, it is (y - k)2 / a2 - (x - h)2 / b2 = 1

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Hyperbola Calculator?

asymptotea line that continually approaches a given curve but does not meet it at any finite distancefocispecial points with reference to which any of a variety of curves is constructedhyperbolaconic section defined as the locus of all points in the plane the difference of whose distances and from two fixed pointsintercept

Example calculations for the Hyperbola Calculator

Hyperbola Calculator Video


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Valentine Belue

Update: 2024-05-18