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(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.