View l3 as a surface of revolution, find an equation of a generating curve on the xy plane which, if revolved around the x axis, will result in l3 Let 13 be the surface withthe equation given by4x²-9y²= 9(z² + 4)22 geven,247²-9y² = 9(2²+4)• TRACE ON TY PLANE:Put 2=0, nehich gives14x²-9y² = 364x²-gy².36 362²-42=1 ANSWERx²y²= 1gThis represents a hyperbola | ANSWER.TRACE OU X2 PLANE:уго,4x² = 9(2²+4)4x²-92²=36PutanehichANSWER.This represents a hyperbola ANSWER• The surface,gines,= 1•TRACE ON.42PLANE:Put x=0, nehich quies,-9y² = 9 (2²+4)= 2 +42²+y² = - + | ANSWER.-4This represents emagénary wiele, whichis obneously [emply] ANSWERTRACEONplanes z = +312Put y = ±312, nehich gives4 (+ 3√2)-ay² = 9(2²+4)+(18) -9y² = 9(²²+4)72-9y² = 9(2²14)36 = 922+ay24 = y² + 2² ANSWER:thisrepresents a circle of raders 2 Centereat Orugen4x²= gy² = 9 (2²+4) represents / HYPERBOLOID OFTWO SHEETS ANSWER.

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Answered: Let 13 be the surface with the equation…

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Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 33E

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Question

View l3 as a surface of revolution, find an equation of a generating curve on the xy plane which, if revolved around the x axis, will result in l3

Let 13 be the surface with
the equation given by
4x²-9y²= 9(z² + 4)
2
2

geven,
2
47²-9y² = 9(2²+4)
• TRACE ON TY PLANE:
Put 2=0, nehich gives
1
4x²-9y² = 36
4x²-gy².
36 36
2²-42=1 ANSWER
x²y²
= 1
g
This represents a hyperbola | ANSWER.
TRACE OU X2 PLANE:
уго,
4x² = 9(2²+4)
4x²-92²=36
Put
a
nehich
ANSWER.
This represents a hyperbola ANSWER
• The surface,
gines,
= 1
•TRACE ON
.
42
PLANE:
Put x=0, nehich quies,
-9y² = 9 (2²+4)
= 2 +4
2²+y² = - + | ANSWER.
-4
This represents emagénary wiele, which
is obneously [emply] ANSWER
TRACE
ON
planes z = +312
Put y = ±312, nehich gives
4 (+ 3√2)-ay² = 9(2²+4)
+(18) -9y² = 9(²²+4)
72-9y² = 9(2²14)
36 = 922+ay2
4 = y² + 2² ANSWER:
this
represents a circle of raders 2 Centere
at Orugen
4x²= gy² = 9 (2²+4) represents / HYPERBOLOID OF
TWO SHEETS ANSWER.

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