Analytic Geometry – Hyperbola

Selasa, 26 Mei 2020

Hyperbola

 

Transverse axis: a

Conjugate axis: b

Foci: F₁(– c, 0), F₂(c, 0)

Distance between the foci: 2c

Eccentricity: e

Asymptotes: s, t

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

 

 

• Equation of a Hyperbola (Standar Form)

      

 

Figure

 

• │r₁ – r₂│= 2a,

    where r₁, r₂ are distances from any point P(x, y) on the hyperbola

     to the two foci.

Figure

 

• Equation of a Asymptoter

     

• c² = a² + b² 

• Eccentricity

      

• Equation of Directricer

     

• Parametric Equation of the Right Branch of a Hyperbola

      

• General Form

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

   Where B² – 4AC > 0 

• General Form with Axes Parsllel to the Coordinate Axes

    Ax² + Bxy + Dx + Ey + F = 0,

    Where AC < 0

 

• Asymptotic Form

     

   In this case, the asymptotes have equation x = 0 and y = 0.

 

Figure

 

 

Sumber

Labels: Mathematician

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