Answer:
Focus of parabola(c) = (0,10) and (0,-10).
The given equation of hyperbola is
[tex]\frac{y^2}{8^2}-\frac{x^2}{a^2}=1[/tex]
b=8
If the equation of Hyperbola is,
[tex]\frac{y^2}{b^2}-\frac{x^2}{a^2}=1[/tex]
then, [tex]b^2=a^2(e^2-1)[/tex]
-------------------------(1)
Where , e is the eccentricity of Hyperbola.
c=a e
10= a e
[tex]e=\frac{10}{a}[/tex]
Putting the value of e, in equation (1)
[tex]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[/tex]
So, the equation of Hyperbola will be
[tex]\frac{y^2}{8^2}-\frac{6^2}{a^2}=1[/tex]
Blank Space = 6
