Hyperbola Calculator

Using the Hyperbola Calculator

This guide will walk you through the steps to use the Hyperbola Calculator effectively. Follow these steps to calculate various properties of a hyperbola.

Step 1: Enter Center Coordinates

• Center x-coordinate (h): Enter the x-coordinate of the center of the hyperbola. This field is required.
• Center y-coordinate (k): Enter the y-coordinate of the center of the hyperbola. This field is also required.

Step 2: Specify the Distances

• Distance from center to vertex (a): Enter the value of ‘a’, which is the distance from the center to each vertex. The value must be greater than or equal to 0.1.
• Distance from center to focus (c): Enter the value of ‘c’, which is the distance from the center to each focus. The value must be greater than or equal to 0.1.

Step 3: Select the Orientation

• Orientation: Choose the orientation of the hyperbola. You can select either “Horizontal (opens left/right)” or “Vertical (opens up/down)”. This field is required.

Step 4: Calculate Results

After entering all the necessary inputs, the calculator will compute and display the following results:

• Value of b: The calculator will determine b using the formula √(c² – a²) and display it to two decimal places.
• Eccentricity (e): Calculated as c/a and displayed to four decimal places.
• Vertices: The coordinates of the vertices will be calculated based on the orientation and displayed to two decimal places.
• Foci: The coordinates of the foci will be computed similarly and displayed to two decimal places.
• Standard Form Equation: The equation of the hyperbola in standard form will be generated based on the inputs. ‘b’ will be calculated internally if not directly visible.
• Asymptotic Slopes: The slopes of the asymptotes, represented as ±b/a or ±a/b depending on orientation, will be displayed to four decimal places.

Follow these steps to effectively use the Hyperbola Calculator for accurate results and insights into the properties of your hyperbola.