AnswersPrecalculusEquations of Hyperbolas

Equations of Hyperbolas Answers

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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
2
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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
3

The graph of a hyperbola is shown.

Question illustration
A
(−12, 0)
B
(0, −5)
C
(0, 0)
D
(13, 0)
4

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

Question illustration
A
10
B
16
C
20
D
26
5

Question text not available

Question illustration
A
= 1
Option A
B
= 1
Option B
C
= 1
Option C
D
= 1
Option D
6

Which statements about the hyperbola are true? Select two options.There is a focus at (0, 12).y = x is an asymptote.y = x is an asymptote.x = is a directrix.y = is a directrix.

Question illustration
A
There is a focus at (0, 12).
B
y = x is an asymptote.
Option B
C
y = x is an asymptote.
Option C
D
x = is a directrix.
Option D
E
y = is a directrix.
Option E
7

Question text not available

Answer not available
8

A hyperbola centered at the origin has a vertex at (−6, 0) and a focus at (10, 0). Which are the equations of the directrices?

Question illustration
A
x = ±
Option A
B
y = ±
Option B
C
x = ±
Option C
D
y = ±
Option D
9

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
10

Question text not available

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

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