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.