Description
Compute c=sqrt(a²-b²) and return a-c cos(parameter) and a+c cos(parameter).
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.
Compute c=sqrt(a²-b²) and return a-c cos(parameter) and a+c cos(parameter).
When to use this tool
Use Ellipse Eccentric Angle Focal Distance when you need a local conic-curve parameter or derivative calculation.
How to use the tool and how it works
- Enter semimajor, semiminor, parameter. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read nearFocusDistance, farFocusDistance. Use the output convention below.
Require semimajor at least positive semiminor and parameter in radians. Compute c=sqrt(a²-b²) and return a-c cos(parameter) and a+c cos(parameter).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| semimajor | Semimajor | Required. Finite number. |
| semiminor | Semiminor | Required. Finite number; strictly above 0. |
| parameter | Ellipse parameter in radians. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| nearFocusDistance | a-c cos(t), distance to the +c focus; may exceed farFocusDistance when cosine is negative. | Required. Finite number. |
| farFocusDistance | a+c cos(t), distance to the -c focus; names are fixed focus labels rather than sorted distances. | Required. Finite number. |
{
"input": {
"semimajor": 5,
"semiminor": 3,
"parameter": 0
},
"output": {
"nearFocusDistance": 1,
"farFocusDistance": 9
}
}Limitations and assumptions
- The output names nearFocusDistance and farFocusDistance refer to fixed (+c, 0) and (-c, 0) focus formulas, not a sorted nearest/farthest pair for every parameter; their order can reverse when cosine is negative.
- 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
- Ellipse Focal Radius Derivative
Return sqrt(a²-b²), mark derivativeDefined only when a>b, and return a/c or -b/c accordingly, otherwise derivative zero.
- Geometry: Ellipse Focus Directrix Gap
Compute c=sqrt(a²-b²), e=c/a, point distance to focus (+c, 0), distance to directrix x=a/e, and focus distance minus e times directrix distance inside result.