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THE FEUTEX TOOLKIT

Hyperbola Foci and Asymptotes

Find focal distance, eccentricity and asymptote slope for a horizontal hyperbola.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaFocus Distance = hypot(a,b); Eccentricity = hypot(a,b)/a; Asymptote Slope = b/a
Sources and model references

Worked example

Inputs

Transverse semi-axis
3 length
Conjugate semi-axis
4 length

Expected results

Focus Distance
5 length
Eccentricity
1.666666667 number
Asymptote Slope
1.333333333 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "a": 3,
  "b": 4
}

Accuracy and scope

Centered horizontal hyperbola x²/a² − y²/b² = 1. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.