Identify the following quadric surface. $z = \frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 16 }$
A) hyperboloid of one sheet
B) elliptic cone
C) elliptic paraboloid
D) hyperboloid of two sheets
E) hyperbolic paraboloid

Question

Quizplus · Accepted Answer

The given equation $z = \frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 16 }$ represents a hyperbolic paraboloid because it has opposite signs for the squared terms and is linear in the remaining variable (z), which is characteristic of hyperbolic paraboloids.

Identify the Following Quadric Surface z=x26−y216z = \frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 16 }z=6x2​−16y2​

Identify the Following Quadric Surface $z = \frac { x ^ { 2 } } { 6 } - \frac { y ^ { 2 } } { 16 }$