```Question 609827
<pre><font face = "Tohoma Ital" size = 3 color = "indigo"><b>
Hi
Note: 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.
hyperbola center= (0,0) vertex= (0,6) and focus= (0,8)  ||opening up and down along the x-axis
{{{(y)^2/6^2 - (x)^2/a^2 = 1}}}     || focus(0,8) and 8 = {{{sqrt(6^2 + a^2)}}}, a = ± {{{sqrt(28)}}}
{{{(y-k)^2/36 - (x)^2/28 = 1}}}
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(0, 0,0.3),
circle(0, 6,0.3),
circle(0, 8,0.3),
graph(300,300,-10,10,-10,10,0, 6sqrt(1+(x)^2/28), -6sqrt(1+(x)^2/28)) )}}}
<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 )```