If your solution to a stated problem does not match the given solution, you should self-critique per instructions at  

http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution: If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

024.

Question: `qQuery problem 7.2.52 (was 7.2.48) identify quadric surface z^2 = x^2 + y^2/2.

Your solution:

Confidence Assessment:

Given Solution:

Self-critique (if necessary):

Self-critique Rating:

Question: `qWhat is the name of this quadric surface, and why?

Your solution:

Confidence Assessment:

Given Solution:

`a f z = c, a constant, then x^2 + y^2/2 = c^2, or x^2 / c^2 + y^2 / (`sqrt(2) * c)^2 = 1. This gives you ellipse with major axis c and minor axis `sqrt(2) * c. Thus for any plane parallel to the x-y plane and lying at distance c from the x-y plane, the trace of the surface is an ellipse.

In the x-z plane the trace is x^2 - z^2 = 0, or x^2 = z^2, or x = +- z. Thus the trace in the x-z plane is two straight lines.

In the y-z plane the trace is y^2 - z^2/2 = 0, or y^2 = z^2/2, or y = +- z * `sqrt(2) / 2. Thus the trace in the y-z plane is two straight lines.

The x-z and y-z traces show you that the ellipses in the 'horizontal' planes change linearly with their distance from the x-y plane. This is the way cones grow, with straight lines running up and down from the apex. Thus the surface is an elliptical cone.

Self-critique (if necessary):

Self-critique Rating:

Question: `qGive the equation of the xz trace of this surface and describe its shape, including a justification for your answer.

Your solution:

Confidence Assessment:

Given Solution:

`a The xz trace consists of the y = 0 points, which for z^2 = x^2 + y^2/2 is z^2 = x^2 + 0^2/2 or just z^2 = x^2.

The graph of z^2 = x^2 consists of the two lines z = x and z = -x in the yz plane.

Self-critique (if necessary):

Self-critique Rating:

Question: `qDescribe in detail the z = 2 trace of this surface.

Your solution:

Confidence Assessment:

Given Solution:

`a If z = 2 then z^2 = x^2 + y^2/2 becomes 2^2 = x^2 + y^2 / 2, or x^2 + y^2 / 2 = 4.

This is an ellipse. If we divide both sides by 4 we can get the standard form:

x^2 / 4 + y^2 / 8 = 1, or x^2 / 2^2 + y^2 / (2 `sqrt(2))^2 = 1.

This is an ellipse with major axis 2 `sqrt(2) in the y direction and 2 in the x direction.