multivariable calculus

posted by .

Consider the surface given by the equation:
2x2 - 3z2 - 4x -4y - 12z + 2 = 0
(a) Write in standard form )
(b) Determine and classify the traces with planes parallel to the xy-, xz- and yz- planes.
(c) Hence classify the surface.

  • multivariable calculus -

    2x^2 - 3z^2 - 4x - 4y - 12z + 2 = 0
    2(x-1)^2-2 - 3(z+2)^2+12 - 4y + 2 = 0
    2(x-1)^2 - 3(x+2)^2 - 4y + 12 = 0
    4(y-3) = 2(x-1)^2 - 3(z+2)^2

    Looks like an hyperbolic paraboloid with vertex at (1,3,-2)

    The traces are an hyperbola in the xz plane, and parabolas in the others.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    I know that standard form is Ax+By=C, but I'm not really sure how to do this problem. All help is welcome. Thanks in advance. Write an equation for each line: through (-1,3) and parallel to y=2x+1 I know that the slop will be 2 because …

    Draw the triangle with vertices D(-2,1), U(4,9), and E(10,1) On a Graph. 2. Find DU, UE, AND DE. (Distance) 3. Classify Triangle DUE by its sides. 4. Write the standard form of the equation of each line: DU, UE, and DE.Also, find the …
  3. Math - intersection of planes

    You are given the following two planes: x+4y-3z-12=0 x+6y-2z-22=0 a) Determine if the planes are parallel b) Fine the line of intersection of the two planes. c) Use the two original equations to determine two other equations that have …
  4. algebra

    given point slope form linear equation to use in answers y-3=3(x+ 1) a.What is equation in standard form of a parallel line that passes through (0, -2)?
  5. algebra 2

    Classify the conic section . Write its equation in standard form. 4x^2-y+3=0?
  6. Analytic Geometry

    Given two planes, discuss the methods used to determine if the planes are parallel, perpendicular, coincident, or none of these.
  7. Calculus

    Consider the planes given by the equations 2y−2x−z=2 x−2y+3z=7 (a) Find a vector v parallel to the line of intersection of the planes. (b)Find the equation of a plane through the origin which is perpendicular to the …
  8. Calculus

    Determine whether the planes are parallel or orthogonal. Equations given: 5x - 3y + z = 4 x + 4y + 7z = 1 How exactly do I solve this?
  9. Algebra

    Given below are equations for 2 planes in R3. 3x1 − 2x2 = 10 x1 + 2x2 + 4x3 = −2 Explain why these two planes must intersect in a line.
  10. Math (Planes)

    Given the equation x + z = 2. Is P parallel to any of the coordinate planes?

More Similar Questions