Business Calc Homework w answers_Part_93

Business Calc Homework w answers_Part_93 - Appendix A5.2 3...

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3. 3 x 2 1 2 y 2 5 6 } x 2 2 } 1 } y 3 2 } 5 1 c 5 ˇ a w 2 w 2 w b w 2 w 5 ˇ 3 w 2 w 2 w 5 1 e 5 } a c } 5 } ˇ 1 3 w } ; F (0, 6 1); directrices are y 5 0 6 } a e }56 56 3 4. 6 x 2 1 9 y 2 5 54 } x 9 2 } 1 } y 6 2 } 5 1 c 5 ˇ a w 2 w 2 w b w 2 w 5 ˇ 9 w 2 w 6 w 5 ˇ 3 w e 5 } a c } 5 } ˇ 3 3 w } 5 } ˇ 1 3 w } ; F ( 6 ˇ 3 w , 0); directrices are x 5 0 6 } a e 3 ˇ 3 w 5. Foci: (0, 6 3), e 5 0.5 c 5 3 and a 5 } c e } 5 } 0 3 .5 } 5 6 b 2 5 36 2 9 5 27 } 2 x 7 2 } 1 } 3 y 6 2 } 5 1 6. Foci: ( 6 8, 0), e 5 0.2 c 5 8 and a 5 } c e } 5 } 0 8 .2 } 5 40 b 2 5 1600 2 64 5 1536 } 16 x 0 2 0 } 1 } 15 y 3 2 6 } 5 1 7. Vertices: ( 6 10, 0), e 5 0.24 a 5 10 and c 5 ae 5 10(0.24) 5 2.4 b 2 5 100 2 5.76 5 94.24 } 1 x 0 2 0 } 1 } 94 y . 2 24 } 5 1 8. Vertices: (0, 6 70), e 5 0.1 a 5 70 and c 5 ae 5 70(0.1) 5 7 b 2 5 4900 2 49 5 4851 } 48 x 5 2 1 } 1 } 49 y 0 2 0 } 5 1 9. Focus: ( ˇ 5 w , 0), Directrix: x 5 } ˇ 9 5 w } c 5 ae 5 ˇ 5 w and } a e } 5 } ˇ 9 5 w } } a e e 2 } 5 } ˇ 9 5 w } } ˇ e 2 5 w } 5 } ˇ 9 5 w } e 2 5 } 5 9 } e 5 } ˇ 3 5 w } . Then PF 5 } ˇ 3 5 w } PD ˇ ( x w 2 w ˇ w 5 w w ) 2 w 1 w ( w y w 2 w 0 w ) 2 w 5 } ˇ 3 5 w } ) x 2 } ˇ 9 5 w } ) ( x 2 ˇ 5 w ) 2 1 y 2 5 } 5 9 } 1 x 2 } ˇ 9 5 w } 2 2 x 2 2 2 ˇ 5 w x 1 5 1 y 2 5 } 5 9 } 1 x 2 2 } ˇ 18 5 w } x 1 } 8 5 1 } 2 } 4 9 } x 2 1 y 2 5 4 } x 9 2 } 1 } y 4 2 } 5 1 10. Focus: ( 2 4, 0), Directrix: x 52 16 c 5 ae 5 4 and } a e } 5 16 } a e e 2 } 5 16 } e 4 2 } 5 16 e 2 5 } 1 4 } e 5 } 1 2 } . Then PF 5 } 1 2 } PD ˇ ( x w 1 w 4 w ) 2 w 1 w ( w y w 2 w 0 w ) 2 w 5 } 1 2 } ) x 1 16 ) ( x 1 4) 2 1 y 2 5 } 1 4 } ( x 1 16) 2 x 2 1 8 x 1 16 1 y 2 5 } 1 4 } ( x 2 1 32 x 1 256) } 3 4 } x 2 1 y 2 5 48 } 6 x 4 2 } 1 } 4 y 8 2 } 5 1 11. e 5 } 4 5 } take c 5 4 and a 5 5; c 2 5 a 2 2 b 2 16 5 25 2 b 2 b 2 5 9 b 5 3; therefore } 2 x 5 2 } 1 } y 9 2 } 5 1 12. The eccentricity e for Pluto is 0.25, e 5 } a c } 5 0.25 5 } 1 4 } take c 5 1 and a 5 4; c 2 5 a 2 2 b 2 1 5 16 2 b 2 b 2 5 15 b 5 ˇ 1 w 5 w ; therefore, } 1 x 6 2 } 1 } 1 y 5 2 } 5 1 is a model of Pluto’s orbit. 13. One axis is from (1, 1) to (1, 7) and is 6 units long; the other axis is from (3, 4) to ( 2 1, 4) and is 4 units long. Therefore, a 5 3, b 5 2 and the major axis is vertical. The center is the point C (1, 4) and the ellipse is given by } ( x 2 4 1) 2 } 1 } ( y 2 9 4) 2 } 5 1; c 2 5 a 2 2 b 2 5 3 2 2 2 2 5 5 c 5 ˇ 5 w ; therefore the foci are F (1, 4 6 ˇ 5 w ), the eccentricity is e 5 } a c } 5 } ˇ 3 5 w } , and the directrices are y 5 4 6 } a e } 5 4 65 4 6 } 9 ˇ 5 5 w } . y x 8 –2 5 –5 3 } 1 } ˇ 3 5 w } 2 y x 5 5 y x 4 2 –2 –4 4 2 –4 –2 3 } 1 } ˇ 1 3 w } 2 ˇ 3 w } 1 } ˇ 1 3 w } 2 Appendix A5.2 461
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14. Using PF 5 e ? PD , we have ˇ ( x w 2 w 4 w ) 2 w 1 w y w 2 w 5 } 2 3 } ) x 2 9 ) ( x 2 4) 2 1 y 2 5 } 4 9 } ( x 2 9) 2 x 2 2 8 x 1 16 1 y 2 5 } 4 9 } ( x 2 2 18 x 1 81) } 5 9 } x 2 1 y 2 5 20 5 x 2 1 9 y 2 5 180 or } 3 x 6 2 } 1 } 2 y 0 2 } 5 1. 15. 9 x 2 2 16 y 2 5 144 } 1 x 6 2 } 2 } y 9 2 } 5 1 c 5 ˇ a w 2 w 1 w b w 2 w 5 ˇ 1 w 6 w 1 w 9 w 5 5 e 5 } a c } 5 } 5 4 } ; asymptotes are y 56} 3 4 } x ; F ( 6 5, 0); directrices are x 5 0 6 } a e }56} 1 5 6 } .
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Business Calc Homework w answers_Part_93 - Appendix A5.2 3...

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