Analytic Geometry – Sphere

Rabu, 10 Juni 2020

Sphere

 

Point coordinater: x, y, z, x₁, y₁, z₁, …

Radius of a sphere: R

Center of a sphere: (a, b, c)

Real numbers: A, D, E, F, M

 

• Equation of a Sphere Centered at the Origin (Standard Form)

    x² + y² + z² = R²

 

 

Figure

 

• Equation of a Circle Centered at Any Point (a, b, c)

   (x – a)² + (y – b)² + (z – c)² = R²

 

• Diameter Form

   (x –x₁) (x –x₂) + (y –y₂) (y –y₂) + (z –z₂) (z –z₂) = 0,

   where

   P₁ (x₁, y₁, z₁),  P₂ (x₂, y₂, z₂) are the ends of a diameter.     

 

• Four Point Form

   

 

• Genera Form

   Ax² + Ay² + Az² + Dx + Ey + Fz + M = 0 (A is nonzero).

  The center of the sphere has coordinater (a, b, c), where

   

  The radius of the sphere is

   

 

Sumber

Labels: Mathematician

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