Build an equation for a hyperboloid of two sheets, Mathematics

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1. Build an equation for a hyperboloid of two sheets with the following properties:

a. The central axis of the hyperboloid is the y-axis

b. The two sheets are 4 units apart, and are mirror images of each other across the xz-plane.

c. 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).)

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