Homework 4 – February 11th
The following are questions about the Interactive Gallery of Quadric Surfaces which can
be found at
http://www.math.uiuc.edu/Courses/math241/quadrics/index.html
.
1.
On the page titled “Interactive Gallery of Quadric Surfaces” [get there by clicking “Home”
in the navigation panel] there are 5 equations.
(a) By browsing the other pages in the
interactive gallery, identify the general equation with each quadric surface is represented.
(b) What changes in the general equation
z
=
Ax
2
+
By
2
to diﬀerentiate between a hyper
bolic paraboloid and an elliptic paraboloid.
2.
Click on “Elliptic Paraboloid” in the navigation panel.
(a) By sliding the blue dots back and forth along the appropriate axes, determine the shape
of the crosssections of the elliptic paraboloid
x
2
+
y
2
=
z
in the planes
x
= 0
,y
= 0 and
z
= 0.
(b) Describe why this surface is called a paraboloid. Additionally, why should
this
surface
be referred to as a
circular
paraboloid, rather than an elliptic paraboloid.
(c) On the second (lower) illustration, change the values to be
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 Fall '08
 Kim
 Math, Calculus

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