SOLUTION: Find the center, vertices,and foci of the hyperbola (4,-1)c given by the equation (x + 1) ^2/9 - (y+4)^2/7 = 1 Please give all necessary steps on how to solve so I can understand.

Algebra ->  Trigonometry-basics -> SOLUTION: Find the center, vertices,and foci of the hyperbola (4,-1)c given by the equation (x + 1) ^2/9 - (y+4)^2/7 = 1 Please give all necessary steps on how to solve so I can understand.      Log On


   

Question 860391: Find the center, vertices,and foci of the hyperbola (4,-1)c given by the equation (x + 1) ^2/9 - (y+4)^2/7 = 1 Please give all necessary steps on how to solve so I can understand. thank you!
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

%28x+%2B+1%29+%5E2%2F+highlight_green%283%5E2%29++-+%28y%2B4%29%5E2%2F7+=+1  C(-1, -4)

Hyperbola %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1opening left and right along y = -4

vertices at (-4,-4)and (2,-4) vertices 3 units left and right of center (-1, -4), 

foci: sqrt%289%2B7%29+=+4 foci 4 units left and right of center (-1, -4)

foci: (-5,-4)and (3,-4)



Standard Form of an Equation of an Hyperbola opening left and right 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 units right and left of center along y = k

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