Math / CALCULATOR

Ellipse Center from General Equation

Ellipse Center from General Equation: explicit measurements, a worked example and input validation.

Runs on your deviceUpdates as you typeFormula & example ↓
01

Your inputs

Adjust the values to explore a different result.

Enter a in ax²+cy²+dx+ey+f=0.
Enter c.
Enter d.
Enter e.
Enter f.

Formula

h=−D/(2A); k=−E/(2C); R=Ah²+Ck²−F; semiaxes=√(R/A), √(R/C).
  • Use the units shown beside each field.
  • Results update automatically whenever you change an input.
  • Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
  • Ideal Euclidean geometry. Use one consistent length unit. Measurements and derived quantities use floating-point arithmetic. Axis-aligned ellipses only; no xy term.

Example Calculation

Example inputs
  • A in Ax²+Cy²+Dx+Ey+F=0: 4
  • C: 9
  • D: -8
  • E: 36
  • F: 4

4x²+9y²−8x+36y+4=0 has center (1,−2) and semiaxes 3 and 2.

Frequently asked questions

How do I use this calculator?

Enter a in ax²+cy²+dx+ey+f=0, c, d, e, f. The result updates automatically. Use Reset to restore the example values.

What method does it use?

h=−D/(2A); k=−E/(2C); R=Ah²+Ck²−F; semiaxes=√(R/A), √(R/C).. Ideal Euclidean geometry. Use one consistent length unit. Measurements and derived quantities use floating-point arithmetic. Axis-aligned ellipses only; no xy term.

Why might a rounded result differ?

The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.

Are my inputs saved online?

No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.

Check the assumptions and units before using this result. Read about calculation methods.