AnswersPrecalculusApplying Vectors in the Plane

Equations of Ellipses Answers

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1
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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
2
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Question text not available

Question illustration
A
points N and P
B
points O and P
C
points Q and R
D
points S and T
3

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)
4

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)
5

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)
6

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.
7

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

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

A
The center is at (−4, 2).
B
The distance between the center and each covertex is 3 units.
C
The vertices are at (−7, 1) and (−1, 1).
D
Each focus is approximately 2.65 units above or below the center.
E
The directrices are horizontal lines approximately 6 units from the center on the major axis.
9

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
10

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 20 units
B
vertical line that is 20 units
C
horizontal line that is 31.25 units
D
vertical line that is 31.25 units

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Equations of Ellipses Answers — Precalculus