Download Understanding Multivariable Calculus PDF

TitleUnderstanding Multivariable Calculus
File Size7.9 MB
Total Pages229
Document Text Contents
Page 228

220

Q
ua

dr
ic

S
ur

fa
ce

s

elliptic paraboloid:
22

2 2 .
yx z

a b

Two positive squared terms set equal to a linear third term.

a = b = 1.

Traces are ellipses in planes parallel to the squared terms
x2, y2 ; traces are parabolas in planes parallel to the plane

z .

22

2 2 .
yx z

a b

a = b = 1.

One positive squared term and one negative squared
term set equal to a linear third term.

Traces are parabolas in the plane parallel to the
x2, y2

z .

An alternative orientation is

2 2

2 2 .
y x z
b a

y

x

z

y

x

y

x

z

x

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