9-4 Ellipses
Write an equation of each ellipse.
11. SOLUTION: The orientation is vertical. The center of the ellipse is at (0, 0). The length of the major axis is 20 units, so a = 10.
The length of the minor axis is 12 units, so b = 6.The equation of the ellipse is
.
13. SOLUTION: The orientation is horizontal. The center of the ellipse is at (–5, –4). The length of the major axis is 14 units, so a = 7.
The length of the minor axis is 10 units, so b = 5.The equation of the ellipse is
.
15. SOLUTION: The orientation is vertical. The center of the ellipse is at (–5, 1).
The length of the major axis is 16 units, so a = 8. The length of the minor axis is 8 units, so b = 4.The equation of the
ellipse is
.
Write an equation of an ellipse that satisfies each set of conditions.
17. vertices at (–6, 4) and (12, 4), co-vertices at (3, 12) and (3, –4)
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The orientation is horizontal. The center of the ellipse is at (3, 4). The length of the major axis is 18 units, so a = 9.
The orientation is vertical. The center of the ellipse is at (–5, 1).
The length of the major axis is 16 units, so a = 8. The length of the minor axis is 8 units, so b = 4.The equation of the
9-4 Ellipses
ellipse is
.
Write an equation of an ellipse that satisfies each set of conditions.
17. vertices at (–6, 4) and (12, 4), co-vertices at (3, 12) and (3, –4)
SOLUTION: The orientation is horizontal. The center of the ellipse is at (3, 4). The length of the major axis is 18 units, so a = 9.
The length of the minor axis is 16 units, so b = 8. The equation of the ellipse is
.
19. center at (–2, 6), vertex at (–2, 16), co-vertex at (1, 6)
SOLUTION: The orientation is vertical.
The value of a is 10 and b is 3.
The equation of the ellipse is
.
21. vertices at (4, 12) and (4, –4), co-vertices at (1, 4) and (7, 4)
SOLUTION: The orientation is vertical. The center of the ellipse is at (4, 4). The length of the major axis is 16 units, so a = 8. The
length of the minor axis is 6 units, so b = 3.The equation of the ellipse is
.
Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse
with the given equation. Then graph the ellipse.
25. SOLUTION: The center of the ellipse is (–6, 3), so h = –6 and k = 3.
2
2
The orientation is vertical, so a = 72 and b = 50.
Thus, the coordinates of the foci are (–6, 7.69) and (–6, –1.69).
The length of the major axis is 2a which is about 16.97 units.
The length of the minor axis is 2b which is about 14.14 units.
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SOLUTION: The orientation is vertical. The center of the ellipse is at (4, 4). The length of the major axis is 16 units, so a = 8. The
9-4 Ellipses
length of the minor axis is 6 units, so b = 3.The equation of the ellipse is
.
Find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse
with the given equation. Then graph the ellipse.
25. SOLUTION: The center of the ellipse is (–6, 3), so h = –6 and k = 3.
2
2
The orientation is vertical, so a = 72 and b = 50.
Thus, the coordinates of the foci are (–6, 7.69) and (–6, –1.69).
The length of the major axis is 2a which is about 16.97 units.
The length of the minor axis is 2b which is about 14.14 units.
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