Question 606918
  <pre><font face = "Tohoma" size = 4 color = "indigo"><b> 
Hi,
Ellipse:
{{{(x-h)^2/a^2 + (y-k)^2/b^2 = 1 }}} where Pt(h,k) is the center.
 a and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center
Foci: (0,-3) and (0,3) {{{center:Pt(0,0)}}},and major axis of 10 is along x = 0
  3 = {{{sqrt(25- a^2)}}}, a = 4  |Note: (Distance from Center along major axis)^2 = 25
{{{(x)^2/4^2 + (y)^2/5^2= 1 }}} 
{{{drawing(300,300,   -10,10,-10,10,  arc(0,0,8,10),
 grid(1),
circle(0, 3,0.3),
circle(0, -3,0.3),
circle(4, 0,0.3),
circle(-4, 0,0.3),
graph( 300, 300, -10,10,-10,10,0))}}}

See below descriptions of various conics

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 and b  are the respective vertices distances from center and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center

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 )