Cylinders And Quadric Surfaces Worksheet With Answers Page 3
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2
3Example Use traces to sketch the graph and identify the surface:
2
2
(a) x = y
+ 4z
2
2
(b) x = y
z
2
2
2
(c)
x
+ 4y
z
= 4
(Answers) (a) Elliptic paraboloid,
(b) Hyperbolic paraboloid,
(c) Hyperboloid of two sheets.
Example Reduce the equation to a standard form, and classify the surface :
2
2
2
x
y
+ z
2x + 2y + 4z + 2 = 0
(Answer) (x
1)
(y
1) + (z + 2) = 2 : Ellipsoid.
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