AnswersPrecalculusConic Sections

Conic Sections Answers

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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
2
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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
3

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
4

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
5

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
6

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
7

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
8

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
9

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
10

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

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