College Trigonometry, 2011a

11.6 Hooked on Conics Again 989
2
9. r =
1−cos(θ)
is a parabola
directrix x = −2 ,vertex(−1, 0)
focus (0, 0), focal diameter 4
4
3
2
1
−4 −3 −2 −1 1 2 3 4
−1
−2
−3
−4
y
x
3
2
10. r = is an ellipse
1+ 1 sin(θ) 2
directrix y = 3 , vertices (0, 1), (0, −3)
center (0, −2),foci(0, 0), (0, −2)
minor axis length 2 √ 3
2+sin(θ) = 3
4
3
2
1
−4 −3 −2 −1 1 2 3 4
−1
−2
−4
y
x
3
2
11. r = is an ellipse
1− 1 cos(θ) 2
directrix x = −3 , vertices (−1, 0), (3, 0)
center (1, 0),foci(0, 0), (2, 0)
minor axis length 2 √ 3
2−cos(θ) = 3
4
3
2
y
2
12. r =
1+sin(θ)
is a parabola
directrix y =2,vertex(0, 1)
focus (0, 0), focal diameter 4
4
3
2
1
y
1
−4 −3 −2 −1 1 2 3 4
−1
x
−4 −3 −2 −1 1 2 3 4
−1
−2
x
−2
−3
−4
−4