Identify the surface $- x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 10$ .
A)ellipsoid but not a sphere
B)hyperboloid of one sheet
C)hyperboloid of two sheets
D)cylinder
E)sphere
F)elliptic but not circular paraboloid
G)cone
H)circular paraboloid (figure of revolution)

Question

Quizplus · Accepted Answer

The given equation $- x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 10$ represents a hyperboloid of two sheets because it has two squared terms with opposite signs and one of them is negative, which is characteristic of a hyperboloid of two sheets.

Identify the Surface −x2+y2−z2=10- x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 10−x2+y2−z2=10

Identify the Surface $- x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 10$