# Quadratic Surfaces - PowerPoint PPT Presentation

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Quadratic Surfaces. Calculus III – Thomas Chapter 12 Section 6. Quadratic Surfaces – General Form: Ax 2 + By 2 + Cz 2 + Dxy + Eyz +Fxz + Gx + Hy + Jz + K = 0 . R. M. E. Revised 2-25-07. Parabolic Cylinder y = x 2. Eliptical Cylinder x 2 + 4z 2 = 4. Hyperbolic Cylinder

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Calculus III – Thomas Chapter 12 Section 6

Quadratic Surfaces – General Form: Ax2 + By2 + Cz2 + Dxy + Eyz +Fxz + Gx + Hy + Jz + K = 0

R. M. E. Revised 2-25-07

Parabolic Cylinder

y = x2

Eliptical Cylinder

x2 + 4z2 = 4

Hyperbolic Cylinder

y2 –z2 = 1

Ellipsoid

Elliptical Paraboloid

x2+y2+z2= 1 a2 b2 c2

x2+y2= 1 a2 b2

Elliptical Cone

Hyperboloids

x2+y2=z2a2 b2 c2

y2–x2=z b2 a2 c

Hyperboliod of one sheet

x2+y2–z2= 1 a2 b2 c2

asymptotic to eliptical cone

Hyperboliod of two sheets

z2–x2–y2= 1 c2 a2 b2