Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist.16x2 - 16y2 - z = 0
A. Elliptic paraboloid; xz-trace: 16x2 - z = 0 (parabola); yz-trace: 16y2 + z = 0 (parabola)
B. Elliptic paraboloid; xz-trace: 16x2 - z = 0 (hyperbola); yz-trace: 16y2 + z = 0 (hyperbola)
C. Elliptic cone; xz-trace: 16x2 - z = 0 (hyperbola); yz-trace: 16y2 + z = 0 (hyperbola)
D. Hyperbolic paraboloid; xz-trace: 16x2 - z = 0 (parabola); yz-trace: 16y2 + z = 0 (parabola)
Answer: D
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A.
B.
C.
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A. +
+
B. +
+
C. +
+
+
D. +