College Algebra 9th txtbk

SECTION 6–2 Ellipse 403
23. 4x 2 y 2 16 24. x 2 4y 2 16
33. The graph is
y
y
y
10
5
5
5
5
x
5
5
x
10
10
x
10
5
5
34. The graph is
y
(a)
y
(b)
y
10
5
5
10
10
x
5
5
x
5
5
x
10
5
(c)
In Problems 25–30, sketch a graph of each equation, find the
coordinates of the foci, and find the lengths of the major and
minor axes.
25. 25x 2 9y 2 225 26. 16x 2 25y 2 400
27. 2x 2 y 2 12 28. 4x 2 3y 2 24
29. 4x 2 7y 2 28 30. 3x 2 2y 2 24
In Problems 31–42, find an equation of an ellipse in the form
if the center is at the origin, and
31. The graph is
32. The graph is
x 2
M y2
N 1
10
10
10
10
10
10
y
y
5
(d)
M, N 7 0
10
10
x
x
35. Major axis on x axis
Major axis length 10
Minor axis length 6
36. Major axis on x axis
Major axis length 14
Minor axis length 10
37. Major axis on y axis
Major axis length 22
Minor axis length 16
38. Major axis on y axis
Major axis length 24
Minor axis length 18
39. Major axis on x axis
Major axis length 16
Distance of foci from center 6
40. Major axis on y axis
Major axis length 24
Distance of foci from center 10
41. Major axis on y axis
Minor axis length 20
Distance of foci from center
42. Major axis on x axis
Minor axis length 14
Distance of foci from center
170
1200
43. Explain why an equation whose graph is an ellipse does not define
a function.
44. Consider all ellipses having (0, 1) as the ends of the minor
axis. Describe the connection between the elongation of the ellipse
and the distance from a focus to the origin.
45. Find an equation of the set of points in a plane, each of whose
distance from (2, 0) is one-half its distance from the line x 8.
Identify the geometric figure.
46. Find an equation of the set of points in a plane, each of whose
distance from (0, 9) is three-fourths its distance from the line
y 16. Identify the geometric figure.