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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Writing Equations of Hyperbolas
Name___________________________________
Date________________ Period____
Use the information provided to write the standard form equation of each hyperbola.
1) x
 y
x y 2) x
 y
x y
3) x
 y
x y 4) x
 y
x y
5)
x
y




6)
x
y





7) Vertices:
(
, 
)
,
(
, 
)
Conjugate Axis is units long
8) Vertices:
(
,  
)
,
(
,  
)
Conjugate Axis is  units long
9) Vertices:
(
,
)
,
(
,
)
Endpoints of Conjugate Axis:
(
,
)
(
, 
)
10) Vertices:
(
,
)
,
(
,
)
Endpoints of Conjugate Axis:
(
,

)
(
,
)
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Worksheet by Kuta Software LLC
11) Vertices:
(
,
)
,
(
, 
)
Foci:
(
,  
)
,
(
,  
)
12) Vertices:
(
,
)
,
(
, 
)
Foci:
(
,  
)
,
(
,  
)
13) Vertices:
(
,
)
,
(
, 
)
Distance from Center to Focus = 
14) Vertices:
(
, 
)
,
(
, 
)
Distance from Center to Focus = 
15) Foci:
(
,  
)
,
(
,  
)
Asymptotes: y

x


y

x


16) Foci:
(
, 
)
,
(
 , 
)
Asymptotes: y
x
y
x
17) Vertices:
(
, 
)
,
(
, 
)
Asymptotes: yx
yx
18) Vertices:
(
,
)
,
(
,
)
Asymptotes: yx
yx
19) Foci:
(
, 
)
,
(
, 
)
Conjugate Axis is  units long
20) Foci:
(
,  
)
,
(
,  
)
Endpoints of Conjugate Axis:
(
, 
)
(
, 
)
21) Foci:
(
,  
)
,
(
,  
)
Points on the hyperbola are  units closer
to one focus than the other
22) Center at
(
, 
)
Transverse axis is vertical and  units long
Conjugate axis is units long
23) Center at
(
, 
)
Transverse axis is vertical; central rectangle
is  units wide and  units tall
24) Vertices:
(
,  
)
,
(
,  
)
Perimeter of Central Rectangle =  
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra 2
Writing Equations of Hyperbolas
Name___________________________________
Date________________ Period____
Use the information provided to write the standard form equation of each hyperbola.
1) x
 y
x y
(
y
)


(
x
)


2) x
 y
x y
(
x
)


(
y
)


3) x
 y
x y
(
y
)


(
x
)


4) x
 y
x y
(
y
)


(
x
)


5)
x
y




x


(
y
)


6)
x
y





(
y
)

x


7) Vertices:
(
, 
)
,
(
, 
)
Conjugate Axis is units long
(
y
)


(
x
)

8) Vertices:
(
,  
)
,
(
,  
)
Conjugate Axis is  units long
(
y
)


(
x
)


9) Vertices:
(
,
)
,
(
,
)
Endpoints of Conjugate Axis:
(
,
)
(
, 
)
(
x
)


(
y
)


10) Vertices:
(
,
)
,
(
,
)
Endpoints of Conjugate Axis:
(
,

)
(
,
)
(
x
)


(
y
)


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Worksheet by Kuta Software LLC
11) Vertices:
(
,
)
,
(
, 
)
Foci:
(
,  
)
,
(
,  
)
(
y
)


(
x
)


12) Vertices:
(
,
)
,
(
, 
)
Foci:
(
,  
)
,
(
,  
)
(
y
)


(
x
)


13) Vertices:
(
,
)
,
(
, 
)
Distance from Center to Focus = 
(
y
)


(
x
)


14) Vertices:
(
, 
)
,
(
, 
)
Distance from Center to Focus = 
(
y
)


(
x
)


15) Foci:
(
,  
)
,
(
,  
)
Asymptotes: y

x


y

x


(
y
)


(
x
)


16) Foci:
(
, 
)
,
(
 , 
)
Asymptotes: y
x
y
x
x


(
y
)


17) Vertices:
(
, 
)
,
(
, 
)
Asymptotes: yx
yx
(
x
)


(
y
)


18) Vertices:
(
,
)
,
(
,
)
Asymptotes: yx
yx
(
x
)


y


19) Foci:
(
, 
)
,
(
, 
)
Conjugate Axis is  units long
(
y
)


(
x
)


20) Foci:
(
,  
)
,
(
,  
)
Endpoints of Conjugate Axis:
(
, 
)
(
, 
)
(
y
)

(
x
)


21) Foci:
(
,  
)
,
(
,  
)
Points on the hyperbola are  units closer
to one focus than the other
(
y
)


(
x
)


22) Center at
(
, 
)
Transverse axis is vertical and  units long
Conjugate axis is units long
(
y
)


(
x
)


23) Center at
(
, 
)
Transverse axis is vertical; central rectangle
is  units wide and  units tall
(
y
)


(
x
)


24) Vertices:
(
,  
)
,
(
,  
)
Perimeter of Central Rectangle =  
(
y
)


(
x
)


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