Question 451542
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi, Assuming the vertices are (0,-6)and (0,6)
Note: Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} 
where Pt(h,k) is a center  with vertices 'b' units up and down from center.
Hyperbola with foci (0,-8) and(0,8) vertices(0,-6)and (0,6)
{{{(y)^2/36 -(x)^2/a^2 =1}}}  C(0,0) with vertices V(0,-6) and V(0,6)
foci (0,-8) and(0,8)  c = sqrt(36 + a^2)= 8   a^2 = 28
{{{(y)^2/36 -(x)^2/28 =1}}}
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(0, 0,0.3),
circle(0, -6,0.3),
circle(0, 6,0.3),
graph(300,300,-10,10,-10,10,0,6sqrt(1+ (1/28)(x)^2),-6sqrt(1+ (1/28)(x)^2)))}}}