LINEAR ALGEBRA II es

NON-DEGENERATE QUADRICS


Plane sections of an ellipsoid.
  The canonical equation of an ellipsoid is:

 $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}=1$
The intersection with planes parallel to the plane YZ (x=cte) will be:
- an ellipse, if |cte|<a; - a point, if |cte|=a; - empty, if |cte|>a.
The intersection with planes parallel to the plane XZ (y=cte) will be:
- an ellipse, if |cte|<b; - a point, if |cte|=b; - empty, if |cte|>b.
The intersection with planes parallel to the plane XY (z=cte) will be:
- an ellipse, if |cte|<c; - a point, if |cte|=c; - empty, if |cte|>c.
Plane sections:


 

 

 
  

 

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Academic Year 2024/2025

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