Question 814677
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Hi,
  {{{(y-k)^2/b^2 - (x-h)^2/a^2 = 1}}} 
{{{9y^2+18y=x^2+6x+18}}}
  {{{9(y+1)^2 - 9 -(x-3)^2 -9 = 18}}}
  {{{9(y+1)^2 - (x-3)^2  = 36}}}
  {{{(y+1)^2/(2^2) - (x-3)^2/(6^2)  = 1}}}  C(3,-1)
Slope of asymptotes = ± b/a = ± 2/6 = ± 1/3
 {{{ y[1]-(-1) = (1/3)(x-3)}}}  |Note: asymptotes go thru the C(3,-1)
0r {{{y[1] = (1/3)x -2}}}
{{{ y[2]-(-1) = (-1/3)(x-3)}}}