Question 875386
 <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi
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, 
Foci are  {{{sqrt(a^2+b^2)}}} =  c- units right and left of center along y = k
& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 
(x-2)^2/36 -(y-3)^2/25 =1  Opening right and Left along y = 3
center:  (2,3)
foci: c = sqrt(36+25) = sqrt(61), F(2+&#8730;61,3)  and   F(2-&#8730;61, 3)
asymptotes: m =  ± b/a = ± 5/6
y - 3 = 5/6(x-2), y = (5/6)x + 4/3
y - 3 = -5/6(x-2), y = (-5/6)x + 14/3
{{{drawing(300,300,   -10,10,-10,12, blue(line(4,10,4,-10)),
 grid(1),
circle(2, 3,0.4),
circle(2-sqrt(61), 3,0.4),
circle(2+sqrt(61), 3,0.4),
graph( 300, 300, -10,10,-10,12,0,3,(5/6)x + 4/3,(-5/6)x + 14/3, 5sqrt((x-2)^2/36 - 1)+3,-5sqrt((x-2)^2/36 -1 )+ 3  ))}}}