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Verizon [17]
3 years ago
5

Find the equation for a hyperbola centered at (0, 0), with foci at (0,-sqrt73)) and (0,-sqrt73)) and vertices at (0, -8) and (0,

8).
Mathematics
1 answer:
DanielleElmas [232]3 years ago
3 0

Answer:

\dfrac{y^2}{64}-\dfrac{x^2}{9}=1 .

Step-by-step explanation:

Since vertices lie on y-axis. So, it is a vertical parabola of the form

\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1

where, (h,k) is center, (h,k\pm c) is focus and (h,k\pm a) is vertex.

Center is (0,0). So, h=0 and k=0.

Foci are (0,\pm \sqrt{73}). So c=\sqrt{73}.

Vertices are (0,\pm 8). So a=8.

We know that,

a^2+b^2=c^2

8^2+b^2=(\sqrt{73})^2

b^2=73-64

b=3

Put h=0,k=0, a=8 and b=3 in equation (1).

\dfrac{(y-0)^2}{8^2}-\dfrac{(x-0)^2}{3^2}=1

\dfrac{y^2}{64}-\dfrac{x^2}{9}=1

Therefore, the required equation is \dfrac{y^2}{64}-\dfrac{x^2}{9}=1 .

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