Hyperbola Equation Calculator

Calculate the standard form equation of a hyperbola and visualize it based on its center, semi-axes, and orientation.

Hyperbola Parameters

Center X (h):

Center Y (k):

Semi-Transverse Axis (a):

Semi-Conjugate Axis (b):

Orientation:

Standard Form of Hyperbola Equation:

Hyperbola Visualization

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 (foci) is constant. The standard form of a hyperbola centered at (h, k) 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, 'a' is the semi-transverse axis, and 'b' is the semi-conjugate axis. This calculator helps you find this equation by inputting the center and semi-axes values. Use the visualization to see how the hyperbola is formed based on these parameters.

For further reading, you can refer to resources on conic sections and analytic geometry.