Answer to Question #15782 in Differential Geometry for Aly Nurmohamed

Question

1.(a) Build an equation for a hyperboloid of two sheets with the following properties:
• The central axis of the hyperboloid is the y-axis
• The two sheets are 4 units apart, and are mirror images of each other across the
xz-plane.
• The hyperboloid intersects the plane y = 3 in a circle of radius 5.
(b) Find an equation for a single curve in the xy-plane which, when rotated around the
y-axis, would produce the hyperboloid built in (a). (Hint, set z = 0 in the equation
from (a).)