Ellipse Standard Form Calculator
The Ellipse Standard Form Calculator builds the standard equation of an ellipse and finds its foci distance, eccentricity, and area. Enter the center and the two semi-axes.
Formula
(x−h)²/a² + (y−k)²/b² = 1; c = √(A²−B²); e = c/A; Area = πab
- A and B are the larger and smaller semi-axes.
- Eccentricity ranges from 0 (circle) toward 1 (very elongated).
Center (0,0), a=5, b=3
Inputs
- Center x (h): 0
- Center y (k): 0
- Semi-axis a (x): 5
- Semi-axis b (y): 3
x²/25 + y²/9 = 1, c = 4, e = 0.8, area ≈ 47.1.
Frequently asked questions
What is the standard form of an ellipse?
(x−h)²/a² + (y−k)²/b² = 1, where (h,k) is the center and a, b are the semi-axes.