Question 1047761
Need to Know:
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.  e = c/a.
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 
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x²/16-y²/4=1

C(0,0)
vertices 'a' units right and left of center C(0,0)
V(4,0) and V(-4, 0)
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Foci are  {{{sqrt(4^2+2^2)}}} =  c- units right and left of center C(0,0) along y = k
c = 2√5
F( 2√5, 0) and F(-2√5, 0)
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Asymptotes Lines passing thru C(0,0), with slopes  m =  ± b/a 

m = ± 2/4 =± 1/2
y = ±(1/2)x 
Sketch in the Hyperbola  opening right and  left
{{{drawing(300,300,   -6, 6, -6, 6, grid(1),

circle(2sqrt(5),0, .2),
circle(-2sqrt(5),0,.2),
circle(0,0, .2),
green(circle(4,0, .25)),
green(circle(-4,0, .25)),
graph( 300, 300, -6, 6, -6, 6,0,.5x, -.5x) )}}}