Question 609019
  <pre><font face = "Tohoma Ital" size = 3 color = "indigo"><b> 
Hi
-3x^2 - 3y^2 + 12x + 96=0
x^2  + y^2 - 4x - 32 =0  ||multiplying thru by -1/3
(x-2)^2 -4 +(y)^2 -32 =0  || completing the Square
{{{(x-2)^2 +(y)^2 = 36 }}} |C(2,0 ) and r = 6
Note: 
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
{{{drawing(300,300,-10,10,-10,10,  grid(1),
circle(2, 0,6.0),
circle(2, 0,0.3),

graph(300,300,-10,10,-10,10,0))}}}
See below descriptions of various conics
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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 )