Concept explainers
Quadric surfaces Consider the following equations of quadric surfaces.
a. Find the intercepts with the three coordinate axes, when they exist.
b. Find the equations of the xy-, xz-, and yz-traces, when they exist.
c. Sketch a graph of the surface.
Ellipsoids
48.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
University Calculus: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
- (a.) Name the given quadric surface and give its axis. (b.) Sketch the surface. (c.) Name its trace on y = -3. - 225x2 + 100y2 + 36z2 = 0arrow_forwardQuadric surfaces Consider the following equations of quadric surfaces. a. Find the intercepts with the three coordinate axes, when they exist. b. Find the equations of the xy-, xz-, and yz-traces, when they exist. c. Identify and sketch a graph of the surface.arrow_forwardUse surface sketching (Find symmetry, intercepts, traces, sections and full sketch of object) to sketch the paraboloid x^2/81 + y^2/81 = z/3.arrow_forward
- Analyze the trace when the surface z = (1/2)x2 + (1/4) y2 is intersected by the indicated planes. Find the coordinates of the focus of the parabola formed when the surface is intersected by the planes given by (a) y = 4 and (b) x = 2.arrow_forwardQuadric surfaces Consider the following equations of quadric surfaces. a. Find the intercepts with the three coordinate axes, when they exist. b. Find the equations of the xy-, xz-, and yz-traces, when they exist. c. Identify and sketch a graph of the surface. x = y2 + z2arrow_forward(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 81 given the plane.x = k Find the trace. Identify the trace. circleellipse hyperbolaparabola y = k Find the trace. Identify the trace. circleellipse hyperbolaparabola z = k Find the trace. Identify the trace. circleellipse hyperbolaparabola Describe the surface from one of the graphs in the table. ellipsoidelliptic paraboloid hyperbolic paraboloidconehyperboloid of one sheethyperboloid of two sheets (b) If we change the equation in part (a) to x2 − y2 + z2 = 81, how is the graph affected? The graph is rotated so that its axis is the x-axis.The graph is rotated so that its axis is the y-axis. The graph is rotated so that its axis is the z-axisThe graph is shifted one unit in the negative y-direction.The graph is shifted one unit in the positive y-direction. (c) What if we change the equation in part (a) to x2 + y2 + 2y − z2 = 80? The graph is rotated so that its axis…arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning