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Quadric Surfaces Math 32 A Lecture for Friday, October 9

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Linear Functions are Simplest!
Linear Functions are Simplest! A line in R 2 : ax+by = c A plane in R 3 : ax + by + cz = d

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Quadratic Functions are Next in order of complexity
Quadratic Functions are Next in order of complexity IN THE PLANE : Quadratic functions define conic sections

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Ellipse: (x/a) 2 + (y/b) 2 = 1
Hyperbola: (x/a) 2 - (y/b) 2 = 1

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Parabola: y = ax 2
Quadric Surfaces in R 3 Ax 2 + By 2 +Cz 2 +axy+bxz+ cyz= 1

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Type of Quadric Surfaces Ax 2 + By 2 +Cz 2 +axy+bxz+ cyz= 1 Elliptic Paraboloids Hyperbolic Paraboliods Ellipsoids Hyperboloids (one or two sheets)

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Unformatted text preview: • Cones and Cylinders Quadric Surfaces In R 3 : Quadric Surfaces What You Should Know • Determine the type of the surface from an equation in standard form What You Should Know • Determine the VERTICAL and HORIZONTAL TRACES of a quadric surface What You Should Know • The type of a surface • VERTICAL and HORIZONTAL TRACES Ellipsoids Horizontal Trace at Height z (x/a) 2 + (y/b) 2 = const. where const = 1 - (z/c) 2 Ellipsoid (x/a) 2 + (y/b) 2 +(z/c) 2 =1 Horizontal and Vertical Traces Hyperboloids Hyperboloids Paraboloids...
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