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Hyperbola (e >1)
Hyperbola (e >1)y
a-a
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab
Hyperbola (e >1)y
a-a
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab
S’(-ae,0) S(ae,0)2 2
22
a bea
Hyperbola (e >1)y
a-a
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab 0,:focus ae
S’(-ae,0) S(ae,0)2 2
22
a bea
Hyperbola (e >1)y
a-a
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab 0,:focus ae
S’(-ae,0) S(ae,0)
eax :sdirectrice
eax
eax
2 22
2
a bea
Hyperbola (e >1)y
xa-a S(ae,0)S’(-ae,0)
eax
eax
xaby x
aby
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab 0,:focus ae
eax :sdirectrice x
aby :asymptotes
2 22
2
a bea
Hyperbola (e >1)y
xa-a S(ae,0)S’(-ae,0)
eax
eax
xaby x
aby
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab 0,:focus ae
eax :sdirectrice x
aby :asymptotes
foci on the y axis
1 If :Note 2
2
2
2
ax
by2 2
22
a bea
Hyperbola (e >1)y
xa-a S(ae,0)S’(-ae,0)
eax
eax
xaby x
aby
Hyperbola:12
2
2
2
by
ax
1 where; 222 eab 0,:focus ae
eax :sdirectrice x
aby :asymptotes
foci on the y axis 1222 eba be,0:focus
eby :sdirectrice
1 If :Note 2
2
2
2
ax
by
xaby :asymptotes
2 22
2
a bea
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
392
aa
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
392
aa 2 2
22
a bea
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
392
aa
2
2
9 169
259
53
e
e
e
2 22
2
a bea
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
392
aa
0,5:foci 35ty eccentrici
59:sdirectrice x
34:asymptotes xy
2 22
2
a bea
2
2
9 169
259
53
e
e
e
e.g.
1169
hyperbola
theofasymptotesand sdirectricefoci,ty,eccentrici theFind22
yx
392
aa
0,5:foci 35ty eccentrici
59:sdirectrice x
34:asymptotes xy
Exercise 6B; 1acd, 2, 3
2 22
2
a bea
2
2
9 169
259
53
e
e
e