Hyperbola Calculator
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 = √9
a = 3
b = √4
b = 2
Calculate asymptote 1:
| Asymptote 1 = | ax |
| b |
| Asymptote 1 = | 3x |
| 2 |
Calculate asymptote 2:
| Asymptote 2 = | -ax |
| b |
| Asymptote 2 = | -3x |
| 2 |
Determine y-intercepts:
y-intercepts = ±a
y-intercepts = ±3
y-intercepts =(0, 3) and (0, -3)
Determine the foci:
Our foci are at (0,c) and (0,-c) where
a2 + b2 = c2
Therefore, c = √a2 + b2
a = √32 + 22
c = √9 + 4
c = √13
c = 3.605551275464
Foci = (0,3.605551275464) and (0,-3.605551275464)
Calculate eccentricity ε
| ε = | c |
| a |
| ε = | 3.605551275464 |
| 3 |
ε = 1.2018504251547
Calculate latus rectum:
| Latus Rectum = | 2b2 |
| a |
| Latus Rectum = | 2(2)2 |
| 3 |
| Latus Rectum = | 2(4) |
| 3 |
| Latus Rectum = | 8 |
| 3 |
Latus Rectum = 2.6666666666667
Calculate semi-latus rectum l:
| l = | Latus Rectum |
| 2 |
| l = | 2.6666666666667 |
| 2 |
l = 1.3333333333333
Final Answers:
hyperbola has a vertical
y-intercepts = (0, 3) and (0, -3)
Foci = (0,3.605551275464) and (0,-3.605551275464)
ε = 1.2018504251547
Latus Rectum = 2.6666666666667
l = 1.3333333333333
What is the Answer?
hyperbola has a vertical
y-intercepts = (0, 3) and (0, -3)
Foci = (0,3.605551275464) and (0,-3.605551275464)
ε = 1.2018504251547
Latus Rectum = 2.6666666666667
l = 1.3333333333333
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 = 1standard 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 pointsinterceptExample calculations for the Hyperbola Calculator
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