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

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