Question

Name and sketch the quadric surfaces y2+9z2 = 9.

Answer #1

Sketch the graphs of the quadratics surfaces defined by the
equations x = z2 - y2 and y2 -
x2 - z2 = 1 on the coordinates systems
below.

(1) Sketch the given surfaces ( for Question (a) and (b) graph
x=0, y=0 and z=2 traces)
(a) x2-4y2=z
(b) y2-4x2-z2=4
(2) state the type of the quadric surface and describe the trace
obtained by intersecting with the given plane.
(x/2)2+(y/5)2-5z2=1, x=0

Consider the surface (elliptic cone) y2=
x2+ 4z2.
(a) Sketch the two coordinate traces corresponding to x= 0 and
z= 0 in R3.
(b) Sketch the trace y= 4.
(c) For any positive number k describe the trace y=k.
(d) Sketch the graph of the surface y2=
x2+ 4z2.

Sketch the graph of each curve by finding surfaces on which they
lie.
(A) <t,tcos(t),tsin(t)>
(B) <cos(t),sin(t),sin(2t)>
(C) <t,cos(t),sin(t)>
Please Sketch in a 3D graph.

Sketch the central field F = (x /(x2 +
y2)1/2)i + (y /(x2 +
y2)1/2) j and the curve C consisting of the
parabola y = 2 − x2 from (−1, 1) to (1, 1) to determine
whether you expect the work done by F on a particle moving along C
to be positive, null, or negative. Then compute the line integral
corresponding to the work.

Find the volume of the solid using a triple
integral.
The solid enclosed between the surfaces x = y2 +
z2 and x = 1 - y2.

Find the maximum and minimum values of
f(x,y)=81x2+y2f(x,y)=81x2+y2 subject to the constraint
4x2+y2=94x2+y2=9.

Problem: Sketch the traces of the quadric surface z = 4x^2 +
6y^2. Include the traces in coordinate planes as well as traces in
planes of the form x = k, y = l, and z = m.

determine the volume of solid object limited by cylinder x2 + y2 =
r2 and y2 + z2 = r2 with r = 1. sketch the integration area!

A curve is given as the intersection of the two surfaces
2x + y + 2z = 8 and (x + 1)2 + y2 / 4 =
1.
Determine the equation of the curve in parameter form.

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