Question 449050
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Hi
{{{(x+4)^2 + (y+7)^2=81}}} Circle C(-4,-7) and radius is 9
See below descriptions of various conics
{{{drawing(300,300, -20,20,-20,20, grid(1), 
circle(-4, -7,0.3),
circle(-4, -7,9),
circle(5, 5,0.3),graph( 300, 300,-20,20,-20,20))}}}

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 and a and b  are the respective vertices distances from center.

Standard Form of an Equation of an Hyperbola opening right andd 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.

Using 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)