AnswersPrecalculusEquations of Hyperbolas

Equations of Hyperbolas Answers

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

Question illustration
A
10
B
16
C
20
D
26
4

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
5

A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39). 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
6

The graph of a hyperbola is shown.

Question illustration
A
(−12, 0)
B
(0, −5)
C
(0, 0)
D
(13, 0)
7

Which graph represents the hyperbola = 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

Question text not available

Question illustration
A
The point (−3, 0) is a focus.
B
The point (3, 0) is a vertex.
C
The transverse axis passes through the point (0, 2).
D
The transverse axis has an endpoint at (5, 0).
9

Which graph represents the hyperbola = 1?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
10

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

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