Hyperbola Equation Calculator

Quickly find the standard form equation of a hyperbola and visualize it. Just input the center, semi-axes, and orientation.

Hyperbola Parameters

Center X (h):

Semi-transverse Axis (a):

Orientation:

Center Y (k):

Semi-conjugate Axis (b):

Standard Form Equation:

Hyperbola Visualization

Understanding Hyperbola Equations

A hyperbola is a type of conic section defined as the set of all points in a plane such that the absolute difference of the distances from two fixed points, called foci, is constant. The standard form equation of a hyperbola depends on its orientation:

Horizontal Hyperbola: $$ rac{(x-h)^2}{a^2} - rac{(y-k)^2}{b^2} = 1 $$
Vertical Hyperbola: $$ rac{(y-k)^2}{a^2} - rac{(x-h)^2}{b^2} = 1 $$

Where:

(h, k) is the center of the hyperbola.
'a' is the semi-transverse axis.
'b' is the semi-conjugate axis.

Use this calculator to easily find the standard form equation by inputting the center (h, k), semi-axes (a, b), and choosing the orientation (horizontal or vertical). The interactive graph helps visualize the hyperbola based on your inputs.

For further reading and more detailed explanations, you can refer to resources like: Wikipedia - Hyperbola, MathWorld - Hyperbola.