Question 860403
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
{{{(y)^2/highlight_green(3^2) - (x-2)^2/16 = 1}}}<u> C(0,0)</u> opening Up and down along x = 0
Vertices: V(0,-3) and V(0,3) {{{highlight_green(3)}}} units up and down from center
foci: F(0,-5) and F(0, 5)  |{{{sqrt(9+16)}}}| = 5 units up and down from center
Asymptotes: slopes  m =  ± 3/4,  thru (0,0), y =  ± (3/4)x 
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,   -10,10,-10,12, 
 grid(1),
circle(0, -3,0.4),
circle(0,3,0.4),
circle(0, -5,0.4),
circle(0, 5,0.4),
graph( 300, 300, -10,10,-10,12,0, .75x, -.75x, 3sqrt((x)^2/16 + 1),-3sqrt((x)^2/16 +1 )))}}}