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.
Elliptic cones
63.
Want to see the full answer?
Check out a sample textbook solutionChapter 12 Solutions
Calculus: Early Transcendentals (2nd Edition)
Additional Math Textbook Solutions
University Calculus: Early Transcendentals (4th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Glencoe Math Accelerated, Student Edition
Calculus and Its Applications (11th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus
- Points of Intersection Sketch the circle x2+y2=4. Then find the values of C so that the parabola y=x2+C intersects the circle at the given number of points. (a) 0 points (b) 1 point (c) 2 points (d) 3 points (e) 4 pointsarrow_forward3) Describe the 3-D surfaces in words and draw a graph. Your description should include the shape, location, and direction/orientation. a. ? = ? b. (? − 1) 2 + (? − 1) 2 = 4 c. ? = ? 2arrow_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
- 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_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_forwardWrite Equations Given a Surface For the above plot of the two sheeted hyperboloid (xa)2−(yb)2−(zc)2=1(xa)2-(yb)2-(zc)2=1, find the parameters a, b and c, each of which is a positive integer between 1 and 6 inclusive.Three points on the surface are ( 18, 8, 4 ), ( 9, 4, 1 ) and ( 12, √4848, 0 ).Ignore the computer noise connecting the two sheets.arrow_forward
- 2. Determine the line of intersection of the two planes: x+y-z-2=0 and 2x-y+3z-1=0. Write the parametric form of the equation of the line and solve each planar equation for z.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_forwardDISCUSS: Collinear Points Suppose that you are given thecoordinates of three points in the plane and you want to seewhether they lie on the same line. How can you do this usingslopes? Using the Distance Formula? Can you think of anothermethod?arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
- Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage