Question 470819
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
Standard Form of an Equation of an Hyperbola is  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} 
where Pt(h,k) is a center  with vertices 'a' units right and left of center.
Asymptotes passing thru the center with slope = ± b/a 
foci being ± sqrt(a^2 + b^2)from center  along axis of symmetry y = k
<img src="http://upload.wikimedia.org/wikipedia/commons/thumb/9/97/Hyperbola_properties.svg/200px-Hyperbola_properties.svg.png">
asymptote slope b/a = 3/4   {{{(x-h)^2/16 - (y-k)^2/9 = 1}}} 
foci (-2,-8) and (8,-8). c = sqrt(16+9) = 5, C(3,-8) {{{(x-3)^2/16 - (y+8)^2/9 = 1}}} 
 {{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(-2, -8,0.3),
circle(8, -8,0.3),
circle(3, -8,0.3),
graph(300,300,-10,10,-10,10,0,-8,3sqrt(((x-3)^2/16) -1)-8,-3sqrt(((x-3)^2/16) -1)-8))}}}