Hyperbola Equation Calculator
Easily calculate the equation of a hyperbola in standard form and visualize it interactively. Input the center, semi-axes, and orientation to get instant results.
Hyperbola Parameters
Enter the parameters to define your hyperbola. Adjust the center, semi-axes, and orientation to explore different shapes.
Equation of the Hyperbola:
Interactive Visualization
Explore the hyperbola graph. Zoom, pan, and hover for details.
Understanding Hyperbola Equations
A hyperbola is a type of conic section defined as the locus of points such that the difference of the distances from two fixed points, called foci, is constant. The standard form of a hyperbola equation depends on its orientation:
- Horizontal Hyperbola: $$\frac{(x - h) ^ 2}{a ^ 2} - \frac{(y - k) ^ 2}{b ^ 2} = 1$$
- Vertical Hyperbola: $$\frac{(y - k) ^ 2}{a ^ 2} - \frac{(x - h) ^ 2}{b ^ 2} = 1$$
Here, (h, k) is the center of the hyperbola, \'a\' is the semi-transverse axis, and \'b\' is the semi-conjugate axis. This calculator helps you find the equation given these parameters and visualizes the hyperbola. Use it to understand how each parameter affects the shape and position of the hyperbola.
For further reading, you can refer to resources like: WolframMathWorld - Hyperbola, Wikipedia - Hyperbola.