5) Classify the surfaces, listing shape, location, and orientation: a. 4(? − 1) 2 + 9(? + 1) 2 + ? 2 = 36 b. 4? 2 − (? − 1) 2 + 16(? + 2) 2 = 9 c. ? = 4? 2 − ? 2 d. ? = 9? 2 + 16? 2 5) Classify the surfaces, listing shape, location, and orientation:a. 4(x- 1)2 +9(y+1)² + z2 = 36b. 4x2 - (y- 1)² + 16(z+ 2)² = 9%3Dc. z = 4x2 - y2d. z = 9x2 + 16y²

Answered: Classify the surfaces, listing shape,…

Classify the surfaces, listing shape, location, and orientation: a. 4(? − 1) 2 + 9(? + 1) 2 + ? 2 = 36 b. 4? 2 − (? − 1) 2 + 16(? + 2) 2 = 9 c. ? = 4? 2 − ? 2 d. ? = 9? 2 + 16

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 38E: Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 6,...

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Question

5) Classify the surfaces, listing shape, location, and orientation: a. 4(? − 1) 2 + 9(? + 1) 2 + ? 2 = 36 b. 4? 2 − (? − 1) 2 + 16(? + 2) 2 = 9 c. ? = 4? 2 − ? 2 d. ? = 9? 2 + 16? 2

5) Classify the surfaces, listing shape, location, and orientation:
a. 4(x- 1)2 +9(y+1)² + z2 = 36
b. 4x2 - (y- 1)² + 16(z+ 2)² = 9
%3D
c. z = 4x2 - y2
d. z = 9x2 + 16y²

Expert Solution

Step 1

(As per bartleby guidelines, for questions containing multiple subparts, only first three subparts will be solved. Please upload other parts separately.)

(a)

Consider the given equation,

$4 {(x - 1)}^{2} + 9 {(y + 1)}^{2} + z^{2} = 36$

Divide the equation by 36,

$\frac{{(x - 1)}^{2}}{9} + \frac{{(y + 1)}^{2}}{4} + \frac{z^{2}}{36} = 1$

Thus, the given function is a vertical ellipsoid with the center $(1, - 1, 0)$ .

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