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.
Hyperbolic paraboloids
59.
Want to see the full answer?
Check out a sample textbook solutionChapter 13 Solutions
Calculus: Early Transcendentals (3rd Edition)
Additional Math Textbook Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Precalculus
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Thomas' Calculus: Early Transcendentals (14th Edition)
- An ellipse is the set of all points in the plane for which the ____ of the distances from two fixed points F1 and F2 is constant. The points F1 and F2 are called the ____ of the ellipse.arrow_forwardAnalyze 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_forward(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_forward
- Use 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(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_forwardIdentify the surface of the equation, show solutions. Choices: A. Elliptic Paraboloid B. Cone C. Sphere D. Cylinder E. None of the abovearrow_forward
- Cylinders and Quadric Surface Sketch the following surfaces.arrow_forwardFind the equation of the surface of revolution when the hyperbola (y^2 / 9) − (z^2 / 4) = 1 is revolved about the y-axis and the z-axis. Sketch the resulting surfaces.arrow_forwardShow complete solution.Let S be the surface with equation y = (4x2/9) + z2 a. Write the equation of the traces of S on the coordinate planes and on the plane y = 4. Identifythese traces.b. Identify the graph of S, then sketch S using the traces. Label all important points on each trace.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