Given the hyperbola below
calculate the equation of the asymptotes
intercepts, foci points
eccentricity and other items.
Simplify
The right side of the equation 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 , , and =
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 = √NAN
a = NAN
b = √NAN
b = NAN
Calculate asymptote 1:
| Asymptote 1 = | ax |
| b |
| Asymptote 1 = | NANx |
| NAN |
Calculate asymptote 2:
| Asymptote 2 = | -ax |
| b |
| Asymptote 2 = | NANx |
| NAN |
Determine y-intercepts:
y-intercepts = ±a
y-intercepts = ±NAN
y-intercepts =(0, NAN) and (0, -NAN)
Determine the foci:
Our foci are at (0,c) and (0,-c) where
a2 + b2 = c2
Therefore, c = √a2 + b2
a = √NAN2 + NAN2
c = √NAN + NAN
c = √NAN
c = NAN
Foci = (0,NAN) and (0,-NAN)
Calculate eccentricity ε
| ε = | c |
| a |
| ε = | NAN |
| NAN |
ε = NAN
Calculate latus rectum:
| Latus Rectum = | 2b2 |
| a |
| Latus Rectum = | 2(NAN)2 |
| NAN |
| Latus Rectum = | 2(NAN) |
| NAN |
| Latus Rectum = | NAN |
| NAN |
Latus Rectum = NAN
Calculate semi-latus rectum l:
| l = | Latus Rectum |
| 2 |
| l = | NAN |
| 2 |
l = NAN
Final Answers:
hyperbola has a vertical
y-intercepts = (0, NAN) and (0, -NAN)
Foci = (0,NAN) and (0,-NAN)
ε = NAN
Latus Rectum = NAN
l = NAN
What is the Answer?
hyperbola has a vertical
y-intercepts = (0, NAN) and (0, -NAN)
Foci = (0,NAN) and (0,-NAN)
ε = NAN
Latus Rectum = NAN
l = NAN
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
Hyperbola Calculator Video
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