Center of Ellipse Calculator
Find an axis-aligned ellipse center and semiaxes from Ax²+Cy²+Dx+Ey+F=0.
Formula
h=−D/(2A); k=−E/(2C); R=D²/(4A)+E²/(4C)−F; sx=√(R/A); sy=√(R/C).
Center x ≈ -(-8)÷(2×(4)) · Center y ≈ -(36)÷(2×(9)) · Horizontal semiaxis ≈ sqrt(((-8)^2÷(4×(4))+(36)^2÷(4×(9))-(4))÷(4))+0÷((-8)^2÷(4×(4))+(36)^2÷(4×(9))-(4)) · Vertical semiaxis ≈ sqrt(((-8)^2÷(4×(4))+(36)^2÷(4×(9))-(4))÷(9))
How to use
- Enter positive A and C.
- Enter D, E and F including signs.
- Read the center and horizontal/vertical semiaxes.
Examples
- 4x²+9y²−8x+36y+4=0 has center (1,−2) and semiaxes 3 and 2.
Frequently asked questions
Are rotated ellipses supported?
No. The equation must have no xy term.
What if A and C are negative?
Multiply the whole equation by −1 first. R must be positive.
Are these full axes?
No. Double each semiaxis for the full axis length.
Sources
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