CALCULATOR
Ellipse Center to Focus Distance from Minor Semiaxis and Axis Gap Calculator
Ellipse Center to Focus Distance from Minor Semiaxis and Axis Gap. Example: Minor semiaxis: 2 m, Axis gap: 1 m gives 2.2360679775 m. Axis-aligned ellipse; positive minor semiaxis, nonnegative axis gap; circle boundary gap0 returns focus distance0. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible.
Axis-aligned ellipse; positive minor semiaxis, nonnegative axis gap; circle boundary gap0 returns focus distance0. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Ellipse focus distance satisfies c²=a²-b²; factor the difference.
Accepted inputs: Minor semiaxis: 0.001 to 10,000 m; Axis gap: 0 to 10,000 m.
Ellipse Center to Focus Distance from Minor Semiaxis and Axis Gap
How the calculation works
c=√(gap(2b+gap)); a=b+gap
Worked example
With minor semiaxis 2 m, axis gap 1 m, ellipse center to focus distance from minor semiaxis and axis gap is 2.236067977 m.
Assumptions and limits
Axis-aligned ellipse; positive minor semiaxis, nonnegative axis gap; circle boundary gap0 returns focus distance0. Only this original stated job is proposed, not full historical source coverage. Input domains and output unit must be visible. Derivation: Ellipse focus distance satisfies c²=a²-b²; factor the difference.