Analytic Geometry – Ellipse

Senin, 25 Mei 2020

Ellipse

 

Semimajor axis: a

Semiminor axis: b

Foci: F₁ (– c, 0), F₂ (c, 0)

Eccentricity: e

Real number: A, B, C, D, E, F, t

Perimeter: L

Area: S

 

• Equation of an Ellipse (Standard Form)

     

Figure

 

• r₁ + r₂ = 2a,

   where r₁, r₂ are distances from any point P(x, y) on the ellipse to the foci.

 

Figure

 

• a² = b² + c²

 

• Eccentricity 

     

 

• Equation of Directrices

     

• Parametric Form

      

• General Form

    Ax² + Bxy + Cy² + Dx + Ey + F = 0,

    Where  B² – 4AC < 0.

 

• General Form with Axes Parallel to the Coordinate Axes

    Ax² + Cy² + Dx + Ey + F = 0,

    Where  AC > 0.

 

• Circumference

    L = 4aE(e),

    Where the function E is the complete integral of the second kind.

 

• Approximate Formulas of the Circumference

     

 

• S = πab

 

Sumber

Labels: Mathematician

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