Question 606785
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
Write the standard equation of this conic section:
y^2-x^2+2y-14x-57
(y^2+2y+1)-1 -(x^2+14x+49)+ 49 - 57 = 0
(y+1)^2 - (x+7)^2 = 9
Standard Form:
{{{(y+1)^2 /9 - (x+7)^2/9 = 1}}}
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.
{{{drawing(300,300,-20,20,-20,20,blue(line(-7,20,-7,-20)),grid(1),
circle(-7, -1,0.5),
circle(-7, 2,0.4),
circle(-7, -4,0.4),
graph( 300, 300, -20,20,-20,20,0,3sqrt(1+ (1/9)(x+7)^2)-1,-3sqrt(1+ (1/9)(x+7)^2)-1 ))}}}