1. Hyperbola (e >1)

2. Hyperbola (e >1)
y
-a a
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b

3. Hyperbola (e >1)
y
S’(-ae,0) -a a S(ae,0)
a 2  b2
e 
2
a2
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b

4. Hyperbola (e >1)
y
S’(-ae,0) -a a S(ae,0)
a 2  b2
e 
2
a2
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b
focus :  ae,0 

5. Hyperbola (e >1)
y
S’(-ae,0) -a a S(ae,0)
a 2  b2
e 
2
a2 a a
x x
e e
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b
focus :  ae,0 
a
directrices : x  
e

6. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
a 2  b2
e 
2
a2 a a
x x
e e
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b
focus :  ae,0 
a b
directrices : x   asymptotes : y   x
e a

7. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
a b
2 2 y2 x2
e 
2 Note : If 2  2  1
a2 a a b a
x x foci on the y axis
e e
Hyperbola: x2 y2
 2 1
where; b 2  a 2 e 2  1 2
a b
focus :  ae,0 
a b
directrices : x   asymptotes : y   x
e a

8. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
a b
2 2 y2 x2
e 
2 Note : If 2  2  1
a2 a a b a
x x foci on the y axis
e e
Hyperbola: a 2  b 2 e 2  1
x2 y2
 2 1 focus : 0,be 
where; b 2  a 2 e 2  1 2
a b
focus :  ae,0  directrices : y  
b
a b e
directrices : x   asymptotes : y   x b
e a asymptotes : y   x
a

9. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16

10. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16
a2  9
a3

11. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16
a2  9 a 2  b2
e2 
a3 a2

12. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16
a2  9 a 2  b2
e2 
a3 a2
9  16
e 
2
9
25
e 
2
9
5
e
3

13. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16
5
 eccentricity 
a2  9 a 2  b2 3
e2 
a3 a2 foci :  5,0 
9  16 9
e 
2
directrices : x  
9 5
4
e 
2 25 asymptotes : y   x
9 3
5
e
3

14. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola   1
9 16
5
 eccentricity 
a2  9 a 2  b2 3
e2 
a3 a2 foci :  5,0 
9  16 9
e 
2
directrices : x  
9 5
4
e 
2 25 asymptotes : y   x
9 3
5
e
3
Exercise 6B; 1acd, 2, 3