Surfaces in Three-Space: Review of Conic Sections and Quadric Surfaces, Exercises of Advanced Calculus

Download Surfaces in Three-Space: Review of Conic Sections and Quadric Surfaces and more Exercises Advanced Calculus in PDF only on Docsity! 1 Surfaces in Three-Space Quick Review of the Conic Sections a) Parabola b) Ellipse c) Hyperbola = 1 2 Surfaces in Three-Space The graph of a 3-variable equation which can be written in the form F(x,y,z) = 0 or sometimes z = f(x,y) (if you can solve for z) is a surface in 3D. One technique for graphing them is to graph cross-sections (intersections of the surface with well-chosen planes) and/or traces (intersections of the surface with the coordinate planes). We already know of two surfaces: a) plane Ax + By + Cz = D b) sphere (x-h)2 + (y-k)2 + (z-l)2 = r2 EX 1 Sketch a graph of z = x2 + y2 and x = y2 + z2.