Question 626966
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
{{{(y+3)^2/5^2-(x-5)^2/2^2=1}}}
 length of the transverse axis(distance between vertices) = 2·5 = 10
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
{{{drawing(300,300,   -20,20,-20,20,blue(line(5,-20,5,20))  ,   
 grid(1),
circle(5, -3,0.4),
circle(5, 2,0.5),
circle(5, -8,0.5),
graph( 300, 300, -20,20,-20,20,0, 5sqrt(1+(x-5)^2/4)-3,-5sqrt(1+(x-5)^2/4)-3 ))}}}