AnswersPrecalculusEquations of Ellipses

Equations of Ellipses Answers

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Which statements about the ellipse are true? Select three options.

A
The center is at (0, 0).
B
The major axis is 4 units long.
C
The vertices are 4 units to the left and right of the center.
D
The foci are units to the left and right of the center on the major axis.
Option D
E
The directrices are vertical lines.
2
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An ellipse has a center at the origin, a vertex along the major axis at (10, 0), and a focus at (8, 0).Which equation represents this ellipse?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
3

Which statements about the ellipse are true? Select three options.

A
The center is at (−2, −5).
B
The distance between the center and each vertex is 10 units.
C
The covertices are at (−2, −4) and (−2, −6).
D
The distance between the center and each focus is units.
Option D
E
The directrices are horizontal lines approximately 5.1 units from the center.
4

The equation represents an ellipse.Which points are the foci of the ellipse?

Question illustration
A
(−16, −6) and (14, −6)
B
(−10, −6) and (8, −6)
C
(−1, −18) and (−1, 6)
D
(−1, −15) and (−1, 3)
6

The equation represents an ellipse.Which points are the approximate locations of the foci of the ellipse? Round to the nearest tenth.

Question illustration
A
(−8, −4.6) and (−8, 2.6)
B
(−2.6, −8) and (4.6, 8)
C
(1, 4.4) and (1, 11.6)
D
(11.6, 1) and (4.4, 1)
8

Question text not available

Question illustration
A
(−2.2, 4) and (8.2, 4)
B
(−0.8, 4) and (5.2, 4)
C
(3, -1.2) and (3, 9.2)
D
(3, 1.3) and (3, 6.7)
9

The equation represents an ellipse.

Question illustration
A
x = −8.6 and x = 8.6
B
x = −6.6 and x = 10.6
C
y = −8.6 and y = 8.6
D
y = −6.6 and y = 10.6
10

The graph of an ellipse is shown.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
11

An ellipse is represented by the equation .Each directrix of this ellipse is a ________________________ from the center on the major axis.

Question illustration
A
horizontal line that is 5 units
B
vertical line that is 5 units
C
horizontal line that is 33.8 units
D
vertical line that is 33.8 units
12

The equation represents an ellipse.Which point is the center of the ellipse?

Question illustration
A
(−9, 5)
B
(−5, 9)
C
(5, −9)
D
(9, −5)
13

The equation represents an ellipse.Which points are the vertices of the ellipse?

Question illustration
A
(−11, 0) and (11, 0)
B
(−1, 0) and (1, 0)
C
(0, −11) and (0, 11)
D
(0, −1) and (0, 1)
14

The equation represents an ellipse.Which points are the vertices of the ellipse?

Question illustration
A
(7, 1) and (7, −5)
B
(7, −10) and (7, 6)
C
(10, −2) and (4, −2)
D
(15, −2) and (−1, −2)

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