Identify and draw a sketch of the surface [(x-2)] ^2 /9+ [(y-3)] ^2 /4-[(z-1)) ^2 /36-1*elliptic hyperboloid of 1 sheet with center at C(2,3,1).O elliptic hyperboloid of 1 sheet with center at C(2,2,1).O elliptic hyperboloid of 1 sheetnone of the above

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Answered: [(z-1) ^2 /36-1* elliptic hyperboloid…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Identify the type of quadric surface defined by the equation and find all x-, y-, and z-intercepts of the resulting graph. Sketch the graph of this quadric surface on paper. The quadric surface is a / an hyperboloid of one sheet 1 x-intercepts when x = 3 1 2 y-intercepts when y = z-intercepts when z = -1 and 4y² - 9x² + z² = 1, ✓ with Enter your answers as comma separated lists, or enter NONE if there are no intercepts of a particular type.
Which of the following is True? (1) x² - 4y² - 9z²+36 = 0. is an equation of a Hyperboloid of Two Sheets (II) x² = 2-y²-z² is an equation of a sphere. (III) z = √√1-x² - y² is an equation of a Circular Cone (IV) z = y² is an equation of a paraboloid (V) x1 is a an equation of a straight line in three - space. (VI) x -2y = 12 is an equation of a plane in three-space O(IV) & (V) (I), (IV) and (V) (III) & (V) (1) & (III) (II) & (VI) (1) & (V) Only (V) All are True
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The left panel of Figure 3 shows an elliptic hyperboloid of two sheets given by 4x² - y² - 2² = 1. The middle panel shows the plane 2x space curves. With the plane removed for clarity, the right panel just shows the space curves and the hyperboloid.The magenta and navy space curves will be referred to as C₁ and C₂ respectively. y + z = k intersecting the two sheets, resulting in two -10 -10 -10 10 10 10 10 10 Zo -10 -10 0 10 Figure 3 The parametrisation used to plot these space curves is 2t2-4t+5 -10 10 Zo 10 -10 10 0 10 x(t) y(t) 4(t - 2) = t z(t) = 3- 4t 2(t-2) a) Find the domain of t for C₁ and C2 (1) དྱེསྱེºེ (2) (3) b) Using equations (1), (2) and (3) as a guide, determine the general space curve parametrisation in terms of k for the case presented above. This doesn't need to involve the 3 equations subbed directly into the hyperboloid/plane equations, just i.e sub the plane equation into the hyperboloid equation, leaving a relationship involving x,y and k; or y,z and k. Also,…

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[(z-1) ^2 /36-1* elliptic hyperboloid of 1 sheet with center at C(2,3,1). elliptic hyperboloid of 1 sheet with center at C(2,2,1). elliptic hyperboloid of 1 sheet none of the above