Question 448807
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Hi
Hyperbola with vertices (4,3) and (2,3) and foci at (0,3) and (6,3)
Opens right and left C(3,3) a = 1
 (x-3)^/1 - (y-3)^2/b^2 =1
foci at (0,3) and (6,3)  c = {{{sqrt(1^2 + b^2)}}} = 3, b^2 = 8
{{{(x-3)^2/1 - (y-3)^2/8 =1 }}}

{{{drawing(300,300,  -10,10,-10,10, grid(1), 
circle(4, 3,0.3),
circle(2, 3,0.3),
graph( 300, 300,-10,10,-10,10,0, 2.83*sqrt((x-3)^2 -1)+3,-2.83*sqrt((x-3)^2 -1)+3 ))}}}

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 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)