Question

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

Answer 1

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

Answer 2

The answer is 6 I just took the test