Using the traces obtained here for l3, provide a hand drawn sketch of l3 and label all important points. For graph reference, 3*sqrt(2) = 4.2 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.

To Sketch: the graph of 4x2-9y2=9(z2+4).

делеп, 47²-9y² = 9(2²+4) -TRACE ON TY PLANE: Put 2=0. 2 4x²-9y² = 36 36 Put 346 Nas w/co x² - y² g This represents a hyperbola 24/0 nehich gives, = 1 TRACE OU X2 PLANE: - = 1 ANSWER. уто, 4x² = 9(2²+4) 47²-92²=36 nehich gives, 2=1 AUSWER This represents o hyperbola ANSWER - The surface, ANSWER •TRALE ON YZ PLANE . Put x=0, nehich quies, -9y² = 9(2²+4) -y²= 2² +4 4 ANSWER Ils represents emagénary wiele, which is obviously [emply] ANSWER TRACE ON planes 2 = ± 31/2 Put y = ±312, nehich gives 4 (+352)²-ay² = 9(2²+4) + (18) -9y² = 9(2²+4) 72-9y²= 9(2²14) 6 = 9₂² +9y² += y² +₂² ANSWER. this reprybents a circle of radens 2 Centers at Orugen 4x²-gy² = 9 (²²+4) represents | HYPERBOLOID OF TWO SHEETS ANSWER.

делеп, 47²-9y² = 9(2²+4) -TRACE ON TY PLANE: Put 2=0. 2 4x²-9y² = 36 36 Put 346 Nas w/co x² - y² g This represents a hyperbola 24/0 nehich gives, = 1 TRACE OU X2 PLANE: - = 1 ANSWER. уто, 4x² = 9(2²+4) 47²-92²=36 nehich gives, 2=1 AUSWER This represents o hyperbola ANSWER - The surface, ANSWER •TRALE ON YZ PLANE . Put x=0, nehich quies, -9y² = 9(2²+4) -y²= 2² +4 4 ANSWER Ils represents emagénary wiele, which is obviously [emply] ANSWER TRACE ON planes 2 = ± 31/2 Put y = ±312, nehich gives 4 (+352)²-ay² = 9(2²+4) + (18) -9y² = 9(2²+4) 72-9y²= 9(2²14) 6 = 9₂² +9y² += y² +₂² ANSWER. this reprybents a circle of radens 2 Centers at Orugen 4x²-gy² = 9 (²²+4) represents | HYPERBOLOID OF TWO SHEETS ANSWER.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 35E

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