SOLUTION: Find the equation in standard form of the hyperbola with vertices at (7,-1_ and (1, -1_ and foci (9,-1_ and (-1, -1). Not sure of any of the steps so please show me steps if possi

Algebra ->  Trigonometry-basics -> SOLUTION: Find the equation in standard form of the hyperbola with vertices at (7,-1_ and (1, -1_ and foci (9,-1_ and (-1, -1). Not sure of any of the steps so please show me steps if possi      Log On


   

Question 860398: Find the equation in standard form of the hyperbola with vertices at (7,-1_ and (1, -1_ and foci (9,-1_ and (-1, -1). Not sure of any of the steps so please show me steps if possible.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Vertices (7,-1) and (1, -1) and foci (9,-1) and (-1, -1) Note: repeat of y = -1

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

%28x-h%29%5E2%2Fa%5E2+-+%28y%2B1%29%5E2%2Fb%5E2+=+1 

Vertices (7,-1) and (1, -1),  h = %287%2B1%29%2F2+= 4  ⇒ foci are 3 units right and left of center (4, -1),  a = 3

%28x-4%29%5E2%2F3%5E2+-+%28y%2B1%29%5E2%2Fb%5E2+=+1

foci (9,-1)_ and (-1, -1). 5 units right and left of center (4, -1) sqrt%289+%2B+b%5E2%29 = 5, b^2 = 16, b = 4

%28x-4%29%5E2%2F3%5E2+-+%28y%2B1%29%5E2%2F4%5E2+=+1



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 units right and left of center along y = k

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