Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist.-9x2 - 9y2 + z2 = 9
A. Hyperboloid of two sheets; xy-trace: -9x2 - 9y2 = 9 (circle); xz-trace: z2 - 9x2 = 9 (hyperbola); yz-trace: z2 - 9y2 = 9 (hyperbola)
B. Ellipsoid; xy-trace: -9x2 - 9y2 = 9 (circle); xz-trace: z2 - 9x2 = 9 (ellipse); yz-trace: z2 - 9y2 = 9 (ellipse)
C. Hyperboloid of two sheets; xz-trace: z2 - 9x2 = 9 (hyperbola); yz-trace: z2 - 9y2 = 9 (hyperbola)
D. Hyperboloid of one sheet; xy-trace: -9x2 - 9y2 = 9 (circle); xz-trace: z2 - 9x2 = 9 (hyperbola); yz-trace: z2 - 9y2 = 9 (hyperbola)
Answer: C
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