(a) Find and identify the traces of the quadric surface x 2 + y 2 ? z 2 = 16 giv
ID: 2869810 • Letter: #
Question
(a) Find and identify the traces of the quadric surface
x2 + y2 ? z2 = 16
given the plane.
x = k
Find the trace.
y = k
Find the trace.
z = k
Find the trace.
(b) If we change the equation in part (a) to
x2 ? y2 + z2 = 16,
how is the graph affected?
A.The graph is rotated so that its axis is the x-axis.
B.The graph is rotated so that its axis is the y-axis.
C.The graph is rotated so that its axis is the z-axis
D.The graph is shifted one unit in the negative y-direction.
E. The graph is shifted one unit in the positive y-direction.
(c) What if we change the equation in part (a) to
x2 + y2 + 2y ? z2 = 15?
A.The graph is rotated so that its axis is the x-axis.
B.The graph is rotated so that its axis is the y-axis.
C.The graph is rotated so that its axis is the z-axis
D.The graph is shifted one unit in the negative y-direction.
E.The graph is shifted one unit in the positive y-direction.
Explanation / Answer
a)hyperbola y^2 -z^2 =16-k^2
hyperbola x^2 -z^2 =16-k^2
circle x^2 +y^2 =16-k^2
b)B.The graph is rotated so that its axis is the y-axis
c)D.The graph is shifted one unit in the negative y-direction.
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