Let . Describe the level surface passing through .
A) Hyperboloid of two sheets
B) Hyperboloid of one sheet
C) Elliptical cone
D) Elliptic paraboloid
E) Hyperbolic paraboloid

Question

Let  . Describe the level surface passing through  .
A) Hyperboloid of two sheets 
B) Hyperboloid of one sheet 
C) Elliptical cone 
D) Elliptic paraboloid 
E) Hyperbolic paraboloid

Quizplus · Accepted Answer

The equation for a hyperboloid of one sheet in general form is:
(x-h)^2/a^2 + (y-k)^2/b^2 - (z-l)^2/c^2 = 1
where (h,k,l) is the center of the hyperboloid and a, b, c are the shape parameters.

Comparing this to the given equation with the point (11ead0bc_8ded_c3d5_99a0_bbdc86086530_TB6988_11) on the level surface, we can see that the center is at (11ead0bc_8ded_9cc4_99a0_8d80d3087cd7_TB6988_11) and the shape parameters are equal. Therefore, the level surface passing through the given point is a hyperboloid of one sheet.

Let Describe the Level Surface Passing Through