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 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola)
B) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola)
C) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16y 2 + z = 0 (parabola)
D) Hyperbolic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16 y 2 + z = 0 (parabola)

Question

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 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola) 
B) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola) 
C) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16y 2 + z = 0 (parabola) 
D) Hyperbolic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16 y 2 + z = 0 (parabola)

Quizplus · Accepted Answer

The Answer of 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 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola) 
B) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (hyperbola); yz-trace: 16y 2 + z = 0 (hyperbola) 
C) Elliptic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16y 2 + z = 0 (parabola) 
D) Hyperbolic paraboloid; xz-trace: 16x 2 - z = 0 (parabola); yz-trace: 16 y 2 + z = 0 (parabola)

Identify the Quadric Surface by Name