Pre-Calc Homework Solutions 461

Pre-Calc Homework Solutions 461 - Appendix A5.2 3 3x 2 c...

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Unformatted text preview: Appendix A5.2 3. 3x 2 c F(0, 4. 6x 2 461 2y 2 a2 6 b2 x2 2 y2 3 1 2 0 1 6 3e c a 3 3 11. e 1e a e c a 3 1 3 4 take c 5 4 and a 5; c 2 9b a2 3; b2 3 1 3 ; 3 16 25 x 25 2 b2 b2 y 9 y 4 2 2 therefore 1 1); directrices are y 9y 2 2 x2 54 9 y2 6 c 1 3 a ; F( a e b 2 9 3, 0); directrices are 3 1 3 4 2 2 4 2 4 x x 0 3 3 3 and a y 36 2 5. Foci: (0, b2 3), e 36 9 0.5 c x 27 27 2 c e 3 0.5 6 12. The eccentricity e for Pluto is 0.25, e take c 40 b2 1 and a 15 b 4; c2 a2 b2 1 x 16 2 1 c 8 e 0.2 y2 1 1536 c a 0.25 b2 1 4 16 y 15 2 6. Foci: ( 8, 0), e b 2 0.2 c 64 8 and a 1600 x2 1536 1600 15; therefore, 1 is a model of Pluto's orbit. y 7. Vertices: ( 10, 0), e c ae x2 100 0.24 a 2.4 b 2 10 and 100 5.76 94.24 5 10(0.24) y2 94.24 1 0.1 a 7 b2 70 4900 49 4851 5 x 8. Vertices: (0, and c x 4851 2 70), e 70(0.1) ae y 4900 2 1 9 5 9 5 9. Focus: ( 5, 0), Directrix: x a e 9 5 c e2 13. One axis is from (1, 1) to (1, 7) and is 6 units long; the ae 5 and 5 e 9 5 3 Then PF (x x2 x2 4 9 ae 9 5 2 e2 e 5 5 PD 3 other axis is from (3, 4) to ( 1, 4) and is 4 units long. . Therefore, a 3, b 2 and the major axis is vertical. The center is the point C(1, 4) and the ellipse is given by 5 3 9 5 2 (x 5)2 5)2 2 y2 5x y2 5 4 (y 0)2 5 x 9 x 9 5 (x 4 1)2 (y 9 4)2 1; c2 a2 b2 32 22 5 c 18 5 5; therefore the foci are F(1, 4 c a 3 5 3 5), the y2 x 9 2 5 2 x 9 y 4 2 x 81 5 eccentricity is e y 4 a e 5 3 , and the directrices are 4 9 5 . 5 1 16 c 16 e 2 (y 0)2 ae 4 and 4 10. Focus: ( 4, 0), Directrix: x a e 16 ae e2 16 (x y2 16 4 e2 PF (x x2 1 PD 2 4)2 1 (x 4 1 1 e . Then 4 2 1 x 16 2 y 8 4)2 8x y2 16)2 32x 1 5 2 5 x2 3 4 1 2 (x 4 2 x y2 48 64 48 y2 256) x ...
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