This conic section calculator tool helps you to easily calculate and visualize the properties of ellipses, parabolas, and hyperbolas.
Conic Sections Calculator
This tool helps you determine the type of conic section given a general second degree equation Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
How to Use the Calculator
Enter the numerical values for coefficients A, B, C, D, E, and F in the respective input fields and click “Calculate”. The calculator will identify the type of conic section represented by the entered values.
How It Works
The calculator determines the type of conic section by analyzing the coefficients of the general quadratic equation. It uses the discriminant B^2 - 4AC to differentiate between circles, ellipses, parabolas, and hyperbolas.
- If the discriminant is positive and
A = C, it is a circle. - If the discriminant is positive and
A != C, it is an ellipse. - If the discriminant is zero, it is a parabola.
- If the discriminant is negative, it is a hyperbola.
- If A and C are both zero, it is a degenerate conic.
Limitations
This calculator assumes that the input is for a real conic section; complex coefficients and determining the position or orientation are not supported. It also does not visualize the conic section, and degenerate cases are not detailed further.