find the vertices, foci, and slopes of each asymptotes for each hyperbola.

Mathematics
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1. x^2/16-y^2/4=1

2. x^2/9-y^2/4=1

Jan 21st, 2015

1. x2/16-y2/4=1

Here a2 =16

a=4

b2=4

b=2

b2 = a2(e2-1)

or a2e2=a2+b2

c2= a2e2=a2+b2 =16+4 =20

c = √20

e =√20/4

Center is (0,0)

Foci  = (√20,0) and (-√20,0)

Vertex= (4,0) and (-4,0)

Asymptotes are

y/2 = ± x/4

Slopes of the asymptotes are 1/ 2 and -1/2

2. x2/9-y2/4=1

Here a2 =9

a=3

b2=4

b=2

b2 = a2(e2-1)

or a2e2=a2+b2

c2=a2+b2 =9+4 =13

c = √13

e =√13/3

Center is (0,0)

Foci  = (√13,0) and (-√13,0)

Vertex= (3,0) and (-3,0)

Asymptotes are

y/2 = ± x/3

Slopes of the asymptotes are 2/3 and -2/3


Jan 21st, 2015

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