Question 668469
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Hi,  Standard Forms are the quidelines
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
 and ±{{{sqrt(a^2-b^2)}}}are the foci distances from center: a > b
(x-3)^2/9 + (y+3)^2/16= 1 C(3,-3), V(0,-3)& V(6,-3), V(3,1) &(3,-7), 
F(3, -3 + sqrt(7)) and F(3,-3-sqrt(7))

{{{drawing(300,300,   -10,10,-10,10,  arc(3,-3,6,8),
 grid(1),
circle(3, -3 + sqrt(7),0.4),
circle(3, -3 - sqrt(7),0.4),
graph( 300, 300, -10,10,-10,10))}}}

Standard Form of an Equation of an Hyperbola opening up and down is:
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} with C(h,k) and vertices 'b' units up and down from center,  2b the length of the transverse axis
Foci {{{sqrt(a^2+b^2)}}}units units up and down from center, along x = h
& Asymptotes Lines passing thru C(h,k), with slopes m =  ± b/a