Question 658044
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi, 
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 variable positioned to correspond with major axis)
 a and b  are the respective vertices distances from center
(0, -1) and (12, -1), C(6,-1) and minor axis of length 6. b = 3 
{{{(x-6)^2/6^2 + (y+1)^2/3^2 = 1 }}} 
{{{drawing(300,300,   -10,15,-10,10,  arc(6,-1,12,6),
 grid(1),
circle(6, -1,0.4),
circle(12, -1,0.4),
graph( 300, 300, -10,15,-10,10))}}}

the vertex form of a Parabola opening up(a>0) or down(a<0), {{{y=a(x-h)^2 +k}}} 
where(h,k) is the vertex  and  x = h  is the Line of Symmetry
{{{(y - 2) = (1/2)(x + 3)^2}}}  x = -3  is the Line of Symmetry