AnswersMO-Algebra II A-CRPerforming Operations with Complex Numbers

Equations of Ellipses Answers

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The center of a circle is 5 units below the origin, and the radius is 10 units. What is the equation of this circle?

A
x2 + (y + 5)2 = 10
B
(x + 5)2 + y2 = 10
C
x2 + (y + 5)2 = 100
D
(x + 5)2 + y2 = 100
2
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The diameter of a circle has endpoints (–3, –10) and (4, –6). What is the equation of the circle?

A
(x + one-half) squared + (y minus 8) squared = StartFraction 65 Over 4 EndFraction
Option A
B
(x minus one-half) squared + (y + 8) squared = StartFraction 65 Over 4 EndFraction
Option B
C
(x + one-half) squared + (y minus 8) squared = 65
Option C
D
(x minus one-half) squared + (y + 8) squared = 65
Option D
3

Review the graph of circle A.

Question illustration
A
(x – 2)2 + y2 = 5
B
(x + 2)2 + y2 = 5
C
(x – 2)2 + y2 = 25
D
(x + 2)2 + y2 = 25
4

A parabola has the focus at (4, 6) and the directrix y = –6. Which equation represents this parabola?

A
(x – 4)2 = 24y
B
(x – 4)2 = y
Option B
C
(x – 4)2 = –24y
D
(x – 4)2 = y
Option D
5

The angle between the generator and the central axis of a double-napped cone is 60°. A plane intersecting the cone makes an angle of 50° with the central axis. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
6

Consider the equation y = (x + 2)2 – 3. What is the length of the focal width of the parabola?

A
1 unit
B
4 units
C
12 units
D
16 units
7

Which graph represents the equation y = – (x – 1)2 + 1?

A
On a coordinate plane, a parabola opens up. It goes through (0, 2), has a vertex at (1, 1), and goes through (2, 2).
Option A
B
On a coordinate plane, a parabola opens down. It goes through (0, 0), has a vertex at (1, 1), and goes through (2, 0).
Option B
C
On a coordinate plane, a parabola opens down. It goes through (negative 2, 0), has a vertex at (negative 1, 1), and goes through (0, 0).
Option C
D
On a coordinate plane, a parabola opens up. It goes through (negative 2, 2), has a vertex at (negative 1, 1), and goes through (0, 2).
Option D
8

The angle between the generator and the central axis of a double-napped cone is 50°. Which conic section is formed when a plane intersects the central axis at 50°?

A
circle
B
ellipse
C
parabola
D
hyperbola
9

The equation (x + 1) = (y – 5)2 is represented by which graph?

Question illustration
A
On a coordinate plane, a parabola opens to the left. It goes through (negative 7, negative 3), has a vertex at (1, negative 5), and goes through (negative 7, negative 7).
Option A
B
On a coordinate plane, a parabola opens to the right. It goes through (7, 7), has a vertex at (negative 1, 5), and goes through (7, 3).
Option B
C
On a coordinate plane, a parabola opens to the right. It goes through (9, negative 3), has a vertex at (1, negative 5), and goes through (9, negative 7).
Option C
D
On a coordinate plane, a parabola opens to the left. It goes through (negative 9, 7), has a vertex at (negative 1, 5), and goes through (negative 9, 3).
Option D
10

Consider the equation (x – 5) = (y – 2)2. What is the equation of the directrix?

Question illustration
A
x = 4.0000
B
x = 4.7500
C
x = 4.6250
D
x = 4.9375
11

The angle between the generator and the central axis of a double-napped cone is 40°. A plane intersects the central axis at an angle between 40° and 90°. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
12

Which graph represents the equation (x – 3)2 + y2 = 16?

A
On a coordinate plane, a circle has a center at (negative 3, 0) and radius 4.
Option A
B
On a coordinate plane, a circle has a center at (negative 3, 0) and radius 16.
Option B
C
On a coordinate plane, a circle has a center at (3, 0) and radius 4.
Option C
D
On a coordinate plane, a circle has a center at (3, 0) and radius 16.
Option D
13

A plane intersecting a double-napped cone is perpendicular to the central axis. Which conic section is formed?

A
circle
B
ellipse
C
hyperbola
D
parabola
14

Review the graph of circle A.

Question illustration
A
(x – 4)2 + (y + 5)2 = 12
B
(x + 4)2 + (y – 5)2 = 12
C
(x – 4)2 + (y + 5)2 = 36
D
(x + 4)2 + (y – 5)2 = 36
15

Consider the equation y – 4 = 2(x + 3)2. Where is the vertex located, and in which direction does the parabola open?

A
vertex: (–3, 4); parabola opens up
B
vertex: (–3, 4); parabola opens to the right
C
vertex: (3, –4); parabola opens up
D
vertex: (3, –4); parabola opens to the right
16

Review the graph of a parabola.

Question illustration
A
2(x + 2) = (y + 3)2
B
2(y + 2) = (x + 3)2
C
–2(y + 2) = (x + 3)2
D
–2(x + 2) = (y + 3)2

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