Question 665083
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Hi,
Need to know Your Standard forms: See below
 ellipse: 96(x+6)^2 +24(y-4)^2 = 96  &#8658; {{{(x+6)^2/1 +(y-4)^2/4 = 1}}}
 hyperbola: 9(x+1)^2 - 16(y+12)^2 =144 &#8658; {{{9(x+1)^2/16 - 16(y+12)^2/9=1}}}
 parabola: x^2 + 12x + 36 = -8y + 8  &#8658;  {{{(x+6)^2= -8(y-1)}}}
 

 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

Standard Form of an Equation of an Hyperbola opening right and  left is:
  {{{(x-h)^2/a^2 - (y-k)^2/b^2 = 1}}} with C(h,k) and vertices 'a' units right and left of center,
   
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
The standard form is {{{(x -h)^2 = 4p(y -k)}}}, where  the focus is (h,k + p)