Identify the quadric surface. z² - x² - y²= 1 A) The graph is a hyperboloid of one sheet. B) The graph is an ellipsoid. C) The graph is an elliptic cone. D) The graph is hyperboloid of two sheets. E) The graph is an elliptic paraboloid.

Question

Quizplus · Accepted Answer

This equation represents a hyperboloid of two sheets, as it is in the form of:
(x/a)^2 - (y/b)^2 - (z/c)^2 = 1
where a = b = c = sqrt((S1/U1/P12/S1/S1/P0)^2 + 1) = sqrt(2), and the negative coefficient (-1) for the (z/c)^2 term indicates that the hyperboloid opens in both the positive and negative z directions.

Identify the Quadric Surface