SOLUTION: find the center, foci, asymptotes and a graph the hyperbola in the space provided: (x-2)^2/36 -(y-3)^2/25 =1 Please Help with this. I really need it. Thank you!

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: find the center, foci, asymptotes and a graph the hyperbola in the space provided: (x-2)^2/36 -(y-3)^2/25 =1 Please Help with this. I really need it. Thank you!      Log On


   

Question 875386: find the center, foci, asymptotes and a graph the hyperbola in the space provided:
(x-2)^2/36 -(y-3)^2/25 =1
Please Help with this. I really need it. Thank you!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

Standard Form of an Equation of an Hyperbola opening right and  left is:

  %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1 with C(h,k) and vertices 'a' units right and left of center, 

Foci are  sqrt%28a%5E2%2Bb%5E2%29 =  c- units right and left of center along y = k

& Asymptotes Lines passing thru C(h,k), with slopes  m =  ± b/a 

(x-2)^2/36 -(y-3)^2/25 =1  Opening right and Left along y = 3

center:  (2,3)

foci: c = sqrt(36+25) = sqrt(61), F(2+√61,3)  and   F(2-√61, 3)

asymptotes: m =  ± b/a = ± 5/6

y - 3 = 5/6(x-2), y = (5/6)x + 4/3

y - 3 = -5/6(x-2), y = (-5/6)x + 14/3