Question 610843
  <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 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
The ellipse is centered at (-1, -3). 
The length of its horizontal axis is 6, and the length of its vertical axis is 4.
{{{(x+1)^2/3^2 + (y+3)^2/2^2 = 1 }}}
{{{drawing(300,300, -10,10,-10,10,    arc (-1,-3,6,4),
 grid(1),
circle(-1,-3,0.3),
graph( 300, 300, -10,10,-10,10   ))}}}

<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 )