SOLUTION: Find the center, vertices, foci, and asymptotes of the hyperbola. {{{9y^2+18y=x^2+6x+18}}} I have found the center, vertices, and foci, but I can't seem to get the correct an

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the center, vertices, foci, and asymptotes of the hyperbola. {{{9y^2+18y=x^2+6x+18}}} I have found the center, vertices, and foci, but I can't seem to get the correct an      Log On


   

Question 814677: Find the center, vertices, foci, and asymptotes of the hyperbola.
9y%5E2%2B18y=x%5E2%2B6x%2B18
I have found the center, vertices, and foci, but I can't seem to get the correct answer for the asymptotes.
Thanks for the help!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

  %28y-k%29%5E2%2Fb%5E2+-+%28x-h%29%5E2%2Fa%5E2+=+1 

9y%5E2%2B18y=x%5E2%2B6x%2B18

  9%28y%2B1%29%5E2+-+9+-%28x-3%29%5E2+-9+=+18

  9%28y%2B1%29%5E2+-+%28x-3%29%5E2++=+36

  %28y%2B1%29%5E2%2F%282%5E2%29+-+%28x-3%29%5E2%2F%286%5E2%29++=+1  C(3,-1)

Slope of asymptotes = ± b/a = ± 2/6 = ± 1/3

 +y%5B1%5D-%28-1%29+=+%281%2F3%29%28x-3%29  |Note: asymptotes go thru the C(3,-1)

0r y%5B1%5D+=+%281%2F3%29x+-2

+y%5B2%5D-%28-1%29+=+%28-1%2F3%29%28x-3%29