LINEAR ALGEBRA II es

NON-DEGENERATE QUADRICS


Plane sections of hyperboloid of one sheet.
The canonical equation of a hyperbolod of one sheet 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:
- a hyperbola, if |cte|≠a. - two lines, if |cte|=a.
The intersection with planes parallel to the plane XZ (y=cte) will be
- a hyperbola, if |cte|≠b. - two lines, if |cte|=b.
The intersection with planes parallel to the plane XY (z=cte) will be:
- an ellipse.  
Plane sections:

Tangent:


 

 

 
  

 

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