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QuadraticSurfaces

QuadraticSurfaces - SECTION 10.6 Surfaces in Space 751...

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Unformatted text preview: SECTION 10.6 Surfaces in Space 751 Elliptic Cone z X xz~trace Trace Plane Ellipse Parallel to xy-plane Hyperbola Parallel to xZ—plane Hyperbola Parallel to yz—plane xy-trace (one point) The axis of the cone corresponds to the variable whose coefficient is negative. The traces in the coordinate planes parallel to this axis are intersecting lines. x l . i yz—trace Elliptic Paraboloid yams 2, ”tram x2 yz Z=P+fi Trace Plane Ellipse Parallel to xy-plane Parabola Parallel to xz-plane Parabola Parallel to yz—plane The axis of the paraboloid corresponds to the variable raised to the first power. X' xy-trace (one point) s r V Hyperbolic Paraboloid Z 2 >62 yz~trace Z:L__ b2 a2 Trace Plane Hyperbola Parallel to xy—plane Parabola Parallel to xz—plane Parabola Parallel to yz—plane The axis of the paraboloid corresponds to the variable raised to the first power. xz‘trace 750 CHAPTER 10 Vectors and the Geometry of Space Ellipsoid- ,x2 _ y2 22 _, .55 4525—2 + g — 1_ ' Trace ,, _ Plane Ellipse _ ,_ Parallel to xy—plane The, surface, is asphdeif . a e b =- c ¢0_ ~ , Ellipse, ;: f ;;Rarallel:_t0 xZeplane‘ - Ellipse , “ :Parallel :to yz—plane , xz-trace yz-trace Trace ‘ Plane 1 Ellipse - ' Parallel to xy-plane _Hyperbola -- _ Parallel to xz—plane Hyperbola, . -Parallel loyz—pla’ne The axis of the Ehyperboloid corresponds to the [variable whose coefficient is negative; ‘ ' " ‘ ' Hyperboloid Of'Two'Sheets , Trace L' Plane- _ ‘Hyperbelay‘r Parallel-to xz—plane Hyperbola, _ Parallel, to yz—plane The axis of the :hyperboloid‘ coefficient is positive. There is ‘ no, trace in ‘the coordinate, plane , perpendicular t9 lhisaxis. , Ellipse I Parallel to’xy-plane corresponds to the variable whose ...
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