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Hyperbola Calculator

Calculate hyperbola properties from equation

Calculate Properties

How to Use

  1. Select the orientation (Horizontal or Vertical)
  2. Enter the center coordinates (h, k)
  3. Enter the semi-axis lengths 'a' and 'b'
  4. Click Calculate to see the hyperbola properties

Hyperbola Equations

A hyperbola is the set of all points where the difference of distances from two fixed points (foci) is constant. The standard equations are:

  • **Horizontal:** (x-h)²/a² - (y-k)²/b² = 1
  • **Vertical:** (y-k)²/a² - (x-h)²/b² = 1

Where (h,k) is the center, 'a' is the distance from center to vertex, and 'b' relates to the conjugate axis.

Frequently Asked Questions

What is the difference between a horizontal and vertical hyperbola?
A horizontal hyperbola opens left and right (x-term is positive), while a vertical hyperbola opens up and down (y-term is positive).
How do I find the foci?
The distance 'c' from center to focus is calculated using c² = a² + b².

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