Question 624475
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
what is the length of the transverse axis of the hyperbola defined by the equation 
(y+3)^2/7^2- (x+3)^2/3^2=1  
length of the transverse axis = 14, the distance between the vertices along x = -3
{{{drawing(300,300,   -10,10,-20,10, blue(line(-3,10,-3,-20)),   
 grid(1),
circle(-3, -3,0.4),
graph( 300, 300, -10,10,-20,10,0,7sqrt(1 +(x+3)^2/3^2) - 3,-7sqrt(1 +(x+3)^2/3^2) - 3 ))}}}

Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} with C(h,k) and vertices 'b' units up and down from center, 2b the length of the transverse axis 
Foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h
& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a

Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} with C(h,k) and vertices 'a' units right and left of center,  2a the length of the transverse axis 
Foci are {{{sqrt(a^2+b^2)}}} units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a