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Identify the Quadric Surface by Name

Question 23

Multiple Choice

Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist.
-16 Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist. -16   - 16   - z = 0 A)  Elliptic cone; xz-trace: 16x<sup>2</sup>  - z = 0 (hyperbola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (hyperbola)   B)  Elliptic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (hyperbola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (hyperbola)   C)  Elliptic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (parabola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (parabola)   D)  Hyperbolic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (parabola) ; yz-trace: 16 y<sup>2</sup> + z = 0 (parabola)   - 16 Identify the quadric surface by name. Find and describe the xy-, xz-, and yz-traces, when they exist. -16   - 16   - z = 0 A)  Elliptic cone; xz-trace: 16x<sup>2</sup>  - z = 0 (hyperbola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (hyperbola)   B)  Elliptic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (hyperbola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (hyperbola)   C)  Elliptic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (parabola) ; yz-trace: 16y<sup>2</sup>  + z = 0 (parabola)   D)  Hyperbolic paraboloid; xz-trace: 16x<sup>2</sup>  - z = 0 (parabola) ; yz-trace: 16 y<sup>2</sup> + z = 0 (parabola)   - z = 0


A) Elliptic cone; xz-trace: 16x2 - z = 0 (hyperbola) ; yz-trace: 16y2 + z = 0 (hyperbola)
B) Elliptic paraboloid; xz-trace: 16x2 - z = 0 (hyperbola) ; yz-trace: 16y2 + z = 0 (hyperbola)
C) Elliptic paraboloid; xz-trace: 16x2 - z = 0 (parabola) ; yz-trace: 16y2 + z = 0 (parabola)
D) Hyperbolic paraboloid; xz-trace: 16x2 - z = 0 (parabola) ; yz-trace: 16 y2 + z = 0 (parabola)

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