CAN YOU PLEASE SHOW ALL WORK

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

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

1. x^{2}/16-y^{2}/4=1

Here a^{2} =16

a=4

b^{2}=4

b=2

b^{2} = a^{2}(e^{2}-1)

or a^{2}e^{2}=a^{2}+b^{2}

c^{2}= a^{2}e^{2}=a^{2}+b^{2} =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. x^{2}/9-y^{2}/4=1

Here a^{2} =9

a=3

c^{2}=a^{2}+b^{2} =9+4 =13

c = √13

e =√13/3

Foci = (√13,0) and (-√13,0)

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

y/2 = ± x/3

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

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