Posted by **cheuk** on Tuesday, March 26, 2013 at 8:33am.

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 -
**Steve**, Tuesday, March 26, 2013 at 11:23am
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.

## Answer this Question

## Related Questions

- Geometry HOMEWORK HELP ME PLEASE! - Draw the triangle with vertices D(-2,1), U(4...
- algebra 2 - Classify the conic section . Write its equation in standard form. 4x...
- Calculus - Use normal vectors to determine the intersection, if any, for each of...
- Calculus - Complete the square to write the equation x^2 + y^2 - 6x - 2y + 4 = 0...
- Algebra one, help me please? - Okay so, I have to write an equation in standard ...
- math/Check! - a. An ellipse is formed by stretching the graph of x^2+ y^2=1 ...
- someone please chek my math! - a. An ellipse is formed by stretching the graph ...
- math - the points (-9,0) and (19,0) lie on parabola. a.) determine an equation ...
- college algebra - Use point-slope form to write the equation of the line with ...
- Algebra - Determine the number of real-number solutions to the equation -2x2 - x...