1. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
Lastly, to find c…

2. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
Hyperbolas with center ( 0 , 0 ). Notice the positive part always leads.

3. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
Graph opens left / right

4. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
Graph opens up / down

5. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
Standard form for each type…

6. HYPERBOLAS
The equation of a hyperbola is almost exactly that of an ellipse. The only change that occurs is there is a minus sign between the terms.
ALSO, be careful, the x and y terms can become switched, so be aware that y could lead.
What we will find for each…
a , b , and c
Center : ( h , k )
Major Axis Vertices : ( x1 , y1 ) , ( x2 , y2 )
Foci : ( x , y )
Asymptote Equation :
These are dashed lines that the graph does not cross…

7. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for

8. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
Center ( x , y )
Major vertices ( x1 , y1 ) , ( x2 , y2 )
Foci ( x , y )
Asymptote Eq.

9. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13
Center ( x , y )
Major vertices ( x1 , y1 ) , ( x2 , y2 )
Foci ( x , y )
Asymptote Eq.

10. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13
Center ( 0 , 0 )
Major vertices ( x1 , y1 ) , ( x2 , y2 )
Foci ( x , y )
Asymptote Eq.

11. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13 ±3
Center ( 0 , 0 )
( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 )
Foci ( x , y )
Asymptote Eq.
x leads so x is Major axis…
adjust h by ± a

12. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13 ±3
Center ( 0 , 0 )
( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 )
Foci ( x , y )
Asymptote Eq.
Foci is on major ( x )…
Adjust x by ± c

13. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13 ±3
Center ( 0 , 0 )
( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 )
Foci ( 0 ± √13 , 0 )
Asymptote Eq.
Foci is on major ( x )…
Adjust x by ± c

14. HYPERBOLAS
Lets jump right in…
EXAMPLE : Find the center, major axis vertices, foci, and asymptote equation for
a = 3
b = 2
c = √13 ±3
Center ( 0 , 0 )
( x ) Major vertices ( 3 , 0 ) , ( - 3 , 0 )
Foci ( 0 ± √13 , 0 )
Asymptote Eq.

15. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for

16. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17

17. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 ) Notice that y leads, so be careful in your order

18. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17 ±1
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
- y is positive so the major axis is y change y by ± b

19. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
±√17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Foci lies on major axis
change y by ± c

20. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :

21. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :
To graph, 1st plot center…

22. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :
Next, plot the major vertices…

23. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :
Next, create a rectangle based on your slope in the asymptote equation…

24. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :
Next, sketch your asymptote lines

25. HYPERBOLAS
EXAMPLE # 2 : Find the center, major axis vertices, foci, and asymptote equation for
A = 4
B = 1
C = √ = √17
Center ( - 4 , 2 )
Major Axis Vertices
( - 4 , 3 ) , ( - 4 , 1 )
Foci ( -4 , 2 ± √17 )
Asymptote equation :
Next, sketch your hyperbola…