Question 675116
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Hi
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,   2a the length of the transverse axis
Foci are {{{sqrt(a^2+b^2)}}} units right and left of center along y = k
25x2+50x-9y2-18y-209=0   || putting into Standard form
 25(x+1)^2 - 9(y+1)^2 - 25 + 9 - 209 = 0
 25(x+1)^2 - 9(y+1)^2 = 225
{{{(x+1)^2/9 -(y+1)^2/25 = 1}}}
center:  C(-1,1)
foci: {{{sqrt(a^2+b^2) = sqrt(34)}}} F(-1+{{{sqrt(34)}}},1)  and F(-1-{{{sqrt(34)}}},1)