find the verticles, foci and slope of the asympototes for each hyperbola.

Mathematics
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1. x^2/36-y^2/1=1

2. x^2/9-y^2/25=1

3. x^2/4-y^2/9=11

Jan 21st, 2015

1. x2/36-y2/1=1

Here a2 =36

a=6

b2=1

b=1

b2 = a2(e2-1)

or a2e2=a2+b2

c2=a2+b2 =36+1 =37

c = √37

e =√37/6

Center is (0,0)

Foci  = (√37,0) and (-√37,0)

Vertex= (6,0) and (-6,0)

Asymptotes are

y/1 = ± x/6

Slopes of the asymptotes are 1/6 and -1/6

2. x2/9-y2/25=1

Here a2 =9

a=3

b2=25

b=5

b2 = a2(e2-1)

or a2e2=a2+b2

c2=a2+b2 =9+25 =34

c = √34

e =√34/3

Center is (0,0)

Foci  = (√34,0) and (-√34,0)

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

Asymptotes are

y/5 = ± x/3

Slopes of the asymptotes are 5/3 and -5/3

3. x2/4-y2/9=11

x2/44-y2/99=1

Here a2 =44

a=2√11

b2=99

b=3√11

b2 = a2(e2-1)

or a2e2=a2+b2

c2=a2+b2 =44+99 =143

c = √143

e =√143/2√11

Center is (0,0)

Foci  = (√143,0) and (-√143,0)

Vertex= (2√11,0) and (-2√11,0)

Asymptotes are

y/√99 = ± x/√44

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


Jan 21st, 2015

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Jan 21st, 2015
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