Hyperbola Properties Calculator

Unravel the characteristics of a hyperbola from its equation. Input the standard form equation to determine the center, semi-axes, and visualize the hyperbola graphically.

Equation Input

Enter the standard form of the hyperbola equation. Examples: (x-2)^2/9 - (y+1)^2/4 = 1 or (y+3)^2/16 - (x-1)^2/25 = 1.

Results

Center (h, k):
Orientation:
Semi-Transverse Axis (a):
Semi-Conjugate Axis (b):

Hyperbola Visualization

Understanding Hyperbola Properties

A hyperbola is a type of conic section defined as the locus of points where the difference of the distances to two fixed points (foci) is constant. The standard form equations are:

  • 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. The orientation (horizontal or vertical) depends on whether the x² or y² term is positive. This tool helps you quickly find these properties from a given equation and visualize the hyperbola.

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