Hyperbola Calculator

Given the hyperbola below

calculate the equation of the asymptotes

intercepts, foci points

eccentricity and other items.

Simplify

Our y coefficient is not 1, Our x coefficient is not 1

Divide all terms by the largest value of Coefficient 1, Coefficient 2, and our right hand term

We divide each term by the maximum of 1, 1, and 1 = 1

1x22 x 1

Simplifying, we get:

Determine transverse axis:

Since our first variable is y

the hyperbola has a vertical transverse axis

Determine the equation of the asymptotes:

a = √0.5

a = 0.70710678118655

b = √0.5

b = 0.70710678118655

Calculate asymptote 1:

Asymptote 1 =	ax
	b

Asymptote 1 =	0.70710678118655x
	0.70710678118655

Asymptote 1 = 1x

Calculate asymptote 2:

Asymptote 2 =	-ax
	b

Asymptote 2 =	-0.70710678118655x
	0.70710678118655

Asymptote 2 = -1x

Determine y-intercepts:

y-intercepts = ±a

y-intercepts = ±0.70710678118655

y-intercepts =(0, 0.70710678118655) and (0, -0.70710678118655)

Determine the foci:

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

a2 + b2 = c2

Therefore, c = √a2 + b2

a = √0.707106781186552 + 0.707106781186552

c = √0.5 + 0.5

c = √1

c = 1

Foci = (0,1) and (0,-1)

Calculate eccentricity ε

ε =	c
	a

ε =	1
	0.70710678118655

ε = 1.4142135623731

Calculate latus rectum:

Latus Rectum =	2b2
	a

Latus Rectum =	2(0.70710678118655)2
	0.70710678118655

Latus Rectum =	2(0.5)
	0.70710678118655

Latus Rectum =	1
	0.70710678118655

Latus Rectum = 1.4142135623731

Calculate semi-latus rectum l:

l =	Latus Rectum
	2

l =	1.4142135623731
	2

l = 0.70710678118655

Final Answers:

hyperbola has a vertical
y-intercepts = (0, 0.70710678118655) and (0, -0.70710678118655)
Foci = (0,1) and (0,-1)
ε = 1.4142135623731
Latus Rectum = 1.4142135623731
l = 0.70710678118655

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What is the Answer?

hyperbola has a vertical
y-intercepts = (0, 0.70710678118655) and (0, -0.70710678118655)
Foci = (0,1) and (0,-1)
ε = 1.4142135623731
Latus Rectum = 1.4142135623731
l = 0.70710678118655

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