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
a3
11. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
a2 9 a 2 b2
e2
a3 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
a3 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
a3 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
a3 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