Analytic Geometry - Quadric Surfaces

Senin, 08 Juni 2020

Quadric Surfaces

 

Point coordinater of the quadric surfaces: x, y, z

Real numbers: A, B, C, a, b, c, k₁, k₂, k₃,, …

 

• General Quadratic Equation

   Ax² + By² + Cz² + 2Fyz + 2Gzx + 2Hxy + 2Px + 2Qy + 2Rz + D = 0

 

• Classification of Quadric Surfaces

  

   Here

     

 

• Real Ellipsoid (Case 1) 

     

 

Figure

 

• Imaginary Ellipsoid (Case 2)

     

• Hyperboloid of 1 sheet (Case 3)

     

Figure

 

• Hyperboloid of 2 sheets (Case 4)

     

Figure

 

• Real Quadric Cone (Case 5)

     

Figure

 

• Imaginary Quadric Cone (Case 6)

     

• Elliptic Paraboloid (Case 7)

     

Figure

 

• Hyperboloid Paraboloid (Case 8)

     

Figure

 

• Real Elliptic Cylinder (Case 9)

     

 

Figure 

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