Ellipse Standard Form Calculator

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The longer half-axis of the ellipse: the distance from the center to the farthest point on the boundary. Must be greater than b for a horizontal ellipse.
The shorter half-axis of the ellipse: the distance from the center to the closest point on the boundary. Must be less than a for a horizontal ellipse (a circle when a = b).
The x-coordinate of the ellipse center. Use 0 if the center is at the origin.
The y-coordinate of the ellipse center. Use 0 if the center is at the origin.
Standard Form Equation
x² / 25 + y² / 9 = 1

The standard conic equation for this ellipse

Area47.1239
Perimeter (circumference)25.527
Eccentricity (e)0.8
Linear eccentricity (c)4
Focal width (latus rectum)3.6
Focus F1(-4, 0)
Focus F2(4, 0)
Vertex V1(-5, 0)
Vertex V2(5, 0)
Co-vertex V3(0, -3)
Co-vertex V4(0, 3)
Directrix 1x = -6.25
Directrix 2x = 6.25
OrientationHorizontal (major axis along x)

Ellipse with a = 5, b = 3, centered at (0, 0).

  • Eccentricity 0.8 describes a moderately elongated ellipse.
  • Horizontal (major axis along x).
  • Area = 47.1239, perimeter = 25.527 (Ramanujan approximation).
  • Foci are at (-4, 0) and (4, 0); any point on the ellipse has the same sum of distances to both foci.

Next stepTo convert to general form, expand the squared terms and collect like terms. To find points on the ellipse, substitute any x in the range [h-a, h+a] and solve for y.

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