X2 t03 02 hyperbola (2013)

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