LINEAR ALGEBRA II es

NON-DEGENERATE QUADRICS


Plane sections of a hyperbolic paraboloid..
The canonical equation of a hyperbolic parabolid is:

 $\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}-z=0$
The intersection with planes parallel to the plane YZ (x=cte) will be:
- a parabola.  
The intersection with planes parallel to the plane XZ (y=cte) will be:
- a parabola.  
The intersection with planes parallel to the plane XY (z=cte) will be:
- a hyperbole, if |cte|≠0. - two lines, if |cte|=0.
Plane sections:

Tangent:


 

 

 
  

 

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Academic Year 2024/2025

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