Let 13 be the surface with the equation given by 4x²-9y²= 9(z²+4)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61018891-1fbc-41a9-b831-1811b4c476c9%2F871cb7d2-529a-4ae2-9250-18b3facc8795%2Fl7vefer_processed.png&w=3840&q=75)
Transcribed Image Text: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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