SOLUTION: Find the equation in standard form of the hyperbola with vertices at (3,0) and (-3,0) and foci (5,0) and (-5,0).

Algebra ->  Trigonometry-basics -> SOLUTION: Find the equation in standard form of the hyperbola with vertices at (3,0) and (-3,0) and foci (5,0) and (-5,0).       Log On


   

Question 860406: Find the equation in standard form of the hyperbola with vertices at (3,0) and (-3,0) and foci (5,0) and (-5,0).
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

vertices at (3,0) and (-3,0) and foci (5,0) and (-5,0).   Note: repeat of y = 0

Hyperbola %28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1opening right and left along y = 0

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

vertices at (3,0) and (-3,0) h = %283+-3%29%2F2+= 0  ⇒ foci are 3 units right and left of center (0,0),  a = 3

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

foci (5,0) and (-5,0).    5 units right and left of center (0,0) sqrt%289+%2B+b%5E2%29 = 5, b^2 = 16, b = 4

%28x%29%5E2%2F3%5E2+-+%28y%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