Thomas Calculus 13th [Solutions]

850 Chapter 11 Parametric Equations and Polar Coordinates
6.
2 2
2 y
2 2
9x 10y 90 x 1 c a b
10 9
10 9 1 c
e 1
a
; F( 1,0);
10
10
directrices are x 0 a
10
e
2
1
10
7.
2 2
2 y
2 2
6x 9y 54 x 1 c a b
9 6
c 3
9 6 3 e ; F 3,0 ;
a 3
directrices are x 0 a
e
3 3
2
3
3
3
8.
2 2
2 y
2 2
169x 25y 4225 x 1 c a b
25 169
c
169 25 12 e 12 ;
a 13
directrices are y 0 a 13 169
e 12 12
13
2
9. Foci: (0, 3), e 0.5 c 3 and
a
c
e
2
2
3
y
6 b 36 9 27 x 1
0.5 27 36
2
10. Foci: ( 8,0), e 0.2 c 8 and
a
c
e
2
2
8
y
40 b 1600 64 1536 x 1
0.2 1600 1536
2
11. Vertices: (0, 70), e 0.1 a 70 and
2
2 y
c ae 70(0.1) 7 b 4900 49 4851 x 1
4851 4900
2
12. Vertices: ( 10,0), e 0.24 a 10 and
2
2 y
c ae 10(0.24) 2.4 b 100 5.76 94.24 x 1
100 94.24
2
13. Focus: 5, 0 , Directrix: x 9 c ae 5 and a 9 ae 9 5 9 2
5
e 5 e .
2 2
5
e 5 e 5 e 5 9 3
2
5
2 2 5
2
2
Then PF PD x 5 y 0 x 9 x 5 y 5 x 9
3 3 5 9 5
2 2 5 5 2 2 2 2
2
5 18 81 4
9 5 5 9 4 y
x x y x x x y x
9 4
1
2
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