Question 608874
  <pre><font face = "Tohoma Ital" size = 3 color = "indigo"><b> 
Hi
hyperbola centered at the origin with a horizontal transverse axis of length 8 units: 8 = 2a 
and a conjugate axis of length 6 units. 6 = 2b
Note: 
 Standard Form of an Equation of an Hyperbola opening right and  left 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.
{{{(x)^2/4^2 - (y)^2/3^2 = 1}}}
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(0, 0,0.3),
circle(-4, 0,0.3),
circle(4, 0,0.3),
graph(300,300,-10,10,-10,10,0,.75x,-.75x, 3sqrt(x^2/16 -1),-3sqrt(x^2/16-1)))}}}
<u>See below descriptions of various conics                         </u>
Standard Form of an Equation of a Circle is {{{(x-h)^2 + (y-k)^2 = r^2}}} 
where Pt(h,k) is the center and r is the radius

 Standard Form of an Equation of an Ellipse is {{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} where Pt(h,k) is the center. (a positioned to correspond with major axis)
 a and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center: a > b

Standard Form of an Equation of an Hyperbola opening right and  left 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.

Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} where Pt(h,k) is a center  with vertices 'b' units up and down from center.

the vertex form of a parabola opening up or down, {{{y=a(x-h)^2 +k}}} where(h,k) is the vertex.
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)

the vertex form of a parabola opening right or left, {{{x=a(y-k)^2 +h}}} where(h,k) is the vertex.
The standard form is {{{(y -k)^2 = 4p(x -h)}}}, where  the focus is (h +p,k )