Ellipse Standard Form Calculator
Convert an axis-aligned ellipse equation to center and squared semiaxes.
Formula
Ax²+By²+Cx+Dy+E=0; h=−C/(2A); k=−D/(2B); q=C²/(4A)+D²/(4B)−E; (x−h)²/(q/A)+(y−k)²/(q/B)=1.
Center h ≈ -(-18)÷(2×(9)) · Center k ≈ -(100)÷(2×(25)) · Horizontal denominator a² ≈ (225)÷(9) · Vertical denominator b² ≈ (225)÷(25)
How to use
- Enter coefficients A,B,C,D,E.
- Read center h,k and the two denominators.
- Insert them into the displayed standard form.
Examples
- 9x²+25y²−18x+100y−116=0 gives center (1,−2), denominators 25 and 9.
Frequently asked questions
Is rotation supported?
No xy term is allowed; the ellipse axes are parallel to the coordinate axes.
Which denominator is horizontal?
a² belongs to (x−h)² and b² to (y−k)², regardless of which is larger.
Which equations are rejected?
Zero quadratic coefficients or nonpositive squared semiaxes do not define a real nondegenerate ellipse.
Sources
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