Question 444459
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Hi, Previously Posted
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.
  {{{(y-3)^2/4 - (x+7)^2/12 = 1}}}  Center(-7,3)
 Foci distance from center = {{{sqrt(4+12) = sqrt(16) = 4}}}
 Foci are (-7,7) and (-7,-1)
  {{{drawing(300,300,-20,20,-20,20,grid(1),
circle(-7, 3,0.4),
circle(-7, 7,0.4),
circle(-7, -1,0.5),
graph( 300, 300, -20,20,-20,20,0,2sqrt(1+ (1/12)(x+7)^2)+3,-2sqrt(1+ (1/12)(x+7)^2)+3 ))}}}