Cylinders and Quadric Surfaces: Examples

1. What type of surface is this: MATH

 

Answer:

 

After simplifying, the equation looks as follows:
MATH

From this we see that the surface is a hyperboloid of two sheets with the y-axis as its axis.

 

 

2. What time of surface is: MATH

 

Answer:

 

After simplifying, the equation looks as follows:
MATH

which tells us that it is an ellipsoid that is centered at (2,-1,1).

 

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