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)
Hyperbola: x2 y2
2 1
where; b 2 a 2 e 2 1 2
a b
focus : ae,0
4. Hyperbola (e >1)
y
S’(-ae,0) -a a S(ae,0)
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
5. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
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
6. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
y2 x2
Note : If 2 2 1
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
7. Hyperbola (e >1) b
b y y x
y x
a a
S’(-ae,0) -a a S(ae,0) x
y2 x2
Note : If 2 2 1
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
8. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
9. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
a2 9
a3
10. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
a 9
2 b 2 16
a3 a 2 e 2 1 16
11. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
a 9
2 b 2 16
a3 a 2 e 2 1 16
9e 2 1 16
16
e 1
2
9
25
e
2
9
5
e
3
12. e.g. Find the eccentricity, foci, directrices and asymptotes of the
x2 y2
hyperbola 1
9 16
5
b 2 16 eccentricity
a 9
2
3
a3 a 2 e 2 1 16 foci : 5,0
9e 2 1 16 directrices : x
9
16 5
e 1
2
4
9 asymptotes : y x
3
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
b 2 16 eccentricity
a 9
2
3
a3 a 2 e 2 1 16 foci : 5,0
9e 2 1 16 directrices : x
9
16 5
e 1
2
4
9 asymptotes : y x
3
25
e
2
9
5
e Exercise 6B; 1acd, 2, 3
3