AnswersPrecalculusEquations of Hyperbolas

Equations of Hyperbolas Answers

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A hyperbola centered at the origin has a vertex at (9, 0) and a focus at (−15, 0). Which are the equations of the asymptotes?

Question illustration
A
y = ±x
Option A
B
y = ±x
Option B
C
y = ±x
Option C
D
y = ±x
Option D
3

The center of a hyperbola is located at the origin. One focus is located at (−50, 0) and its associated directrix is represented by the line x= .What is the equation of the hyperbola?

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

Question text not available

Question illustration
A
The point (3.6, 0) is the directrix.
B
The point (−3.6, 0) is the center.
C
The point (2, 0) is a focus.
D
The point (−2, 0) is a vertex.
5

Which graph represents the hyperbola = 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
6

Which is a true statement comparing the graphs of = 1 and = 1?

Question illustration
A
The foci of both graphs are the same points.
B
The lengths of both transverse axes are the same.
C
The directrices of = 1 are horizontal while the directrices of = 1 are vertical.
Option C
D
The vertices of are on the y-axis while the vertices of are on the x-axis.
Option D
7

A hyperbola centered at the origin has a vertex at (0,−40) and a focus at (0, 41). Which are the equations of the asymptotes?

Question illustration
A
y = ±x
Option A
B
y = ±x
Option B
C
y = ±x
Option C
D
y = ±x
Option D
8

The equation represents a hyperbola centered at the origin with a directrix of .

Question illustration
A
10
B
16
C
20
D
26
9

Question text not available

Question illustration
A
(0, −26)
B
(0, −24)
C
(0, 25)
D
(0, 30)
10

The graph of a hyperbola is shown.

Question illustration
A
(−12, 0)
B
(0, −5)
C
(0, 0)
D
(13, 0)

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