Description
Use b/a for horizontal-transverse or a/b for vertical-transverse asymptote slope and return both signs.
A conic curve has parameters tied to a chosen axis system and parameterization. Parametric angle, polar angle, focus distance, tangent, and normal describe different relationships and cannot be interchanged without their definitions.
Use b/a for horizontal-transverse or a/b for vertical-transverse asymptote slope and return both signs.
When to use this tool
Use Hyperbola Asymptote Direction Slope when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter a, b, verticalTransverse. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read positiveSlope, negativeSlope. Use the output convention below.
Require positive a and b. Use b/a for horizontal-transverse or a/b for vertical-transverse asymptote slope and return both signs.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| a | A | Required. Finite number; strictly above 0. |
| b | B | Required. Finite number; strictly above 0. |
| verticalTransverse | Vertical Transverse | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| positiveSlope | Positive Slope | Required. Finite number. |
| negativeSlope | Negative Slope | Required. Finite number. |
{
"input": {
"a": 4,
"b": 3,
"verticalTransverse": false
},
"output": {
"positiveSlope": 0.75,
"negativeSlope": -0.75
}
}Limitations and assumptions
- A is the transverse semiaxis and b the conjugate semiaxis under the selected orientation; the hyperbola is assumed centered on aligned axes and no translation, rotation, or input curve is validated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the full conic equation and coordinate transform for rotated or translated curves. Check semiaxis ordering, parameter units, and degeneracy before interpreting a local tangent or focus identity.
References
Similar or alternative tools
- Geometry: Ellipse Parametric Tangent Direction
Differentiate (a cos t, b sin t), returning the tangent vector and its normalized unitTangent inside result.
- Parabola Parametric Tangent Normal Pair
Return tangent [2 × scale × parameter, 2 × scale] and a perpendicular normal [-2 × scale, 2 × scale × parameter].