CALCULATOR
Axis-Aligned Ellipse Center Coordinate Calculator
Axis-Aligned Ellipse Center Coordinate Calculator — change the supplied values to calculate axis-aligned ellipse center coordinate.
Only axis-aligned positive diagonal quadratic terms, no xy term; coefficients A/B dimensionless and D/E in coordinate units. Center only; F may yield an empty locus. 0=x, 1=y.
Accepted inputs: A: 0.01 to 100 number; B: 0.01 to 100 number; D: -100 to 100 units; E: -100 to 100 units; Coordinate: choose x coordinate (0), y coordinate (1).
How the calculation works
center=(-D/(2A),-E/(2B))
Complete separate squares in Ax²+By²+Dx+Ey+F=0, A,B>0.
Worked example
With a 2 number, b 4 number, d -8 units, e 12 units, coordinate x coordinate, axis-aligned ellipse center coordinate is 2 units.
Assumptions and limits
Only axis-aligned positive diagonal quadratic terms, no xy term; coefficients A/B dimensionless and D/E in coordinate units. Center only; F may yield an empty locus. 0=x, 1=y.