Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

Solution:- We have to Sketch the surfaces ASSORTED 16y2 + 9z2 = 4x2

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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

Section10.6: The Three-dimensional Coordinate System

Problem 41E: Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?

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Sketch the surfaces ASSORTED 16y² + 9z² = 4x²

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Step 1

Solution:- We have to Sketch the surfaces ASSORTED 16y² + 9z² = 4x²

Step 2

we have;

$16 y^{2} + 9 z^{2} = 4 x^{2} d i v i d e d b y 144 i n b o t h o f s i d e s \frac{16 y^{2}}{144} + \frac{9 z^{2}}{144} = \frac{4 x^{2}}{144} \frac{y^{2}}{9} + \frac{z^{2}}{16} = \frac{x^{2}}{36} \frac{y^{2}}{3^{2}} + \frac{z^{2}}{4^{2}} = \frac{x^{2}}{6^{2}} \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = \frac{x^{2}}{a^{2}} a = \pm 6 b = \pm 3 c = \pm 4$

The above equation is general equation of cone having vertex (0,0,0). and cones opens up along x-axis.

the graph of the cone is

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