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

You have 1 free calculations remaining

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?

asymptote: a line that continually approaches a given curve but does not meet it at any finite distance
foci: special points with reference to which any of a variety of curves is constructed
hyperbola: conic section defined as the locus of all points in the plane the difference of whose distances and from two fixed points
intercept