Ellipse Equation Calculator

How to Use the Ellipse Equation Calculator

This guide provides a comprehensive step-by-step approach on how to use the Ellipse Equation Calculator to determine various properties and the equation of an ellipse. Follow the steps carefully to ensure accurate results.

Step 1: Input the Center Coordinates

• Locate the input field labeled Center X-coordinate (h). Enter the x-coordinate of the center of your ellipse. This value is required and must be a number, allowing you to adjust in steps of 0.1.

• Next, find the field labeled Center Y-coordinate (k) to input the y-coordinate of the center. Again, this is a required numeric input with steps of 0.1.

Step 2: Input the Length of the Semi-major and Semi-minor Axes

• Enter the length of the semi-major axis in the Semi-major axis (a) field. Ensure the value is at least 0.1 and input should also be in steps of 0.1.

• Similarly, input the length of the semi-minor axis in the Semi-minor axis (b) field. This value cannot be less than 0.1 and should also increment in steps of 0.1.

Step 3: Calculate Results

After providing the necessary inputs, the calculator computes the following results:

• Standard Form Equation: This displays the standard equation of the ellipse based on your inputs.
• Area: Calculated as π times the semi-major axis length times the semi-minor axis length. The result is displayed with two decimal places and in square units.
• Approximate Perimeter: Uses the approximation formula 2 * π * √((a² + b²) / 2) and shows the result rounded to two decimal places in units.
• Eccentricity: The calculation shows the measure of how much the ellipse deviates from being circular, displayed with four decimal precision.
• Focal Length: Determined by the formula 2 * √|a² – b²| and is expressed with two decimal places in units.

These results allow you to thoroughly analyze the properties of your ellipse based on the input parameters defined.