34. Hyperboloid of one sheet a. Find a parametrization for the hyperboloid of one sheet x² + y? – z? = 1 in terms of the angle 0 associated with the circle x2 + y² = r² and the hyperbolic parameter u associated with the hyperbolic function r² – z? = 1. (Hint: cosh? u - sinh? u = 1.) b. Generalize the result in part (a) to the hyperboloid (x²/a²) + (y²/b²) - (?/2) = 1.

34. Hyperboloid of one sheet a. Find a parametrization for the hyperboloid of one sheet x² + y? – z? = 1 in terms of the angle 0 associated with the circle x2 + y² = r² and the hyperbolic parameter u associated with the hyperbolic function r² – z? = 1. (Hint: cosh? u - sinh? u = 1.) b. Generalize the result in part (a) to the hyperboloid (x²/a²) + (y²/b²) - (?/2) = 1.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.CT: Test

Problem 8CT: Determine whether the statement is true or false. a A right circular cone has exactly two bases. b...

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