AnswersPrecalculusEquations of Hyperbolas

Equations of Hyperbolas — Unit test Answers

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1
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The equation represents a hyperbola centered at the origin with a focus of (0,-10). What is the value of b?

Question illustration
A
4
B
6
C
10
D
12
2
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What is the center of a circle represented by the equation (x−5)2+(y+6)2=42?

A
(−6,5)
B
(−5,6)
C
(5,−6)
D
(6,−5)
3

One focus of a hyperbola is located at (−1, 7). One vertex of the hyperbola is located at (−1, 5). The center is (−1, −3).What is the equation of the hyperbola?

A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
4

The foci and the vertices of the hyperbola are labeled.

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
5

What is the radius of a circle whose equation is x2+y2+8x−6y+21=0?

A
2 units
B
3 units
C
4 units
D
5 units
6

Question text not available

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
7

Which features describe the graph of =1? Select two options.a focus at (104, 0)a focus at (0,−96)a vertex at (−40, 0)a vertex at (0, 96)the center at (0, 0)

Question illustration
A
a focus at (104, 0)
B
a focus at (0,−96)
C
a vertex at (−40, 0)
D
a vertex at (0, 96)
E
the center at (0, 0)
8

The graph of a hyperbola is shown.

Question illustration
A
9 units
B
12 units
C
18 units
D
24 units
9

A parabola and its directrix are shown on the graph.

Question illustration
A
(0,2)
B
(0,–2)
C
(2,0)
D
(–2,0)
10

Which graph represents the equation x2 = 8y?

A
On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 8), and a directrix at y = negative 8.
Option A
B
On a coordinate plane, a parabola opens up. It has a vertex at (0, 0), a focus at (0, 2), and a directrix at y = negative 2.
Option B
C
On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (2, 0), and a directrix at x = negative 2.
Option C
D
On a coordinate plane, a parabola opens to the right. It has a vertex at (0, 0), a focus at (8, 0), and a directrix at x = negative 8.
Option D
11

What is the positive slope of the asymptote of = 1? The positive slope of the asymptote is .

Answer not available
12

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
13

Two circles are concentric if they have the same center.

Question illustration
A
(x – 4)2 + (y – 6)2 = 4
B
(x – 4)2 + (y – 6)2 = 16
C
(x – 6)2 + (y – 4)2 = 16
D
(x – 6)2 + (y – 4)2 = 4
14

A parabola has a vertex at the origin. The focus of the parabola is located at (–2,0).

A
y = 2
B
x = 2
C
y = –2
D
x = –2
15

On a coordinate plane, a parabola opens to the left. It has a vertex at (0, 0), a focus at (negative 2, 0), and a directrix at x = 2.

Question illustration
A
y2 = –2x
B
y2 = –8x
C
x2 = –2y
D
x2 = –8y

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