Quadric Surfaces Graphing in 3 Dimensions

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Quadric SurfacesGraphing in 3 Dimensions

• Lesson 10.2

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A Point in 3D

• Points graphed with respect to three axes

z
y
(3,2 6)
x
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Graphing a Plane in 3D

• Given2x - 3y 4z 12
• Determine intercepts
• z intercept when x, y 0
• y intercept when x, z 0
• x intercept when y, z 0

3
6
-4
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Graphing a Plane in 3D

• Consider the equation x y 7
• z can take on any value
• Results in plane
• through the line x y 7on the x-y plane
• parallel to z axis

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Equation of a Sphere

• Given(x a)2 (y b)2 (z c)2 r2
• Center at (a, b, c)
• radius r

c


a
b
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Locate This Sphere

• Given
• Complete the square

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Graphing in 3D

• Solve for z
• Change calculator mode to 3D graphing
• Enter equation in x and y into the Z screen

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Graphing in 3D

• Equation gives hemisphere
• note only one 3D graph at a time
• Calculator takes some time to graph all the lines
  of the wire frame model
• Image can be rotated
• hold down cursor wheel for continuous rotation

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Graphing in 3D

• Note variety of settings for graphing window
• viewing angle
• number of grid lines(more lines, longertime to
  graph)
• Use F1-Format to turnaxes on/off

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Cylinders

• Consider a curve on a plane (here, x-y plane)
• line through the curve, not on the plane
• generates a wall by tracing the line along the
  curve
• Result is a cylinder

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Cylinders

• Curve can be
• parabola
• hyperbola
• any function

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Quadric Surfaces

• Consider possible versions of
• Sphere
• Ellipsoid
• Hyperbolic paraboloid
• Hyperboloid (one or two sheets)
• Elliptic paraboloid
• See pg 683

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Assignment

• Lesson 10.2
• Page 684
• Exercises 1, 7, 9, 13-22, 25, 33, 43