Ellipse #1

The ellipse is a curved line forming a closed loop, where the sum of the distances from two points (foci) to every point on the line is constant.

We can generate an SVG ellipse 2 ways: using the 'ellipse' shape command, or using a 'path' command.

Some Ellipse Terms and Formulae

• F = distance from each focus to center on the major axis
• R₁ = major axis (a line through both foci)
• R₂ = minor axis (a line perpendicular to major axis through the center)
• a = semi-major axis (R₁ / 2)
• b = semi-minor axis (R₂ / 2)
• C = center of ellipse
• (x/a)² + (y/b)² = 1
• x = acosθ, y = bsinθ
• Eccentricity (e): how much the curve deviates from being circular.
  - circle e = 0
  - ellipse e > 0; e < 1
  - parabola e = 1
  - hyperbola e > 1
  
• Distance from C to either Focus (F₁ or F₂)
• Approximate perimeter (p) :
  p ≅ 2𝝅 √(a² + b²) / 2

If both radii are known the foci can be found.

These 2 foci are represented by the 2 blue circles at F₁ (x=170.627460668062282) and F₂ (x=329.372539331937718)

The distance between F₁ and F₂ = 79.372539331937718 x 2 = 158.745078663875436

In our ellipse

• F = √R₁² - R₂² (distance from center to focal point)
  = √120 - √90
  = √14400 - √8100
  = √6300 = 79.372539331937718
  also known as linear eccentricity
• e = √1 - b²/a² (where a=semi-major axis; b=semi-minor axis)