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aev [14]
3 years ago
9

The equation = 1 represents a hyperbola centered at the origin with a focus of (0,−10).

Mathematics
2 answers:
drek231 [11]3 years ago
8 0

Answer:

Focus of parabola(c) = (0,10) and (0,-10).

The given equation of hyperbola is

  \frac{y^2}{8^2}-\frac{x^2}{a^2}=1

b=8

If the equation of Hyperbola is,

  \frac{y^2}{b^2}-\frac{x^2}{a^2}=1

then, b^2=a^2(e^2-1)

                                          -------------------------(1)

Where , e is the eccentricity of Hyperbola.

c=a e

10= a e

e=\frac{10}{a}

Putting the value of e, in equation (1)

8^2=a^2[\frac{10}{a}]^2-1]\\\\ 64=a^2 \times \frac{100}{a^2}-a^2\\\\ a^2=100-64\\\\ a^2=36\\\\ a=\pm 6

So, the equation of Hyperbola will be

\frac{y^2}{8^2}-\frac{6^2}{a^2}=1

Blank Space = 6

vladimir1956 [14]3 years ago
4 0

The answer is 6 I just took the test

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