SOLUTION: A hyperbola has vertices (4,0) and (-4,0).Its foci are located at (√(20),0) and (-√(20),0).Find the equation of the hyperbola.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A hyperbola has vertices (4,0) and (-4,0).Its foci are located at (√(20),0) and (-√(20),0).Find the equation of the hyperbola.      Log On


   

Question 391748: A hyperbola has vertices (4,0) and (-4,0).Its foci are located at (√(20),0) and (-√(20),0).Find the equation of the hyperbola.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,         

 hyperbola with vertices (4,0) and (-4,0) 

Opens right and left along the x-axis with center at Pt(0,0)

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 where Pt(h,k) is a center  with vertices 'a' units right and left of center.

  x^2/16 - y^2 /b^2 = 1

foci at (-c,0) and (c,0) where c^2 = a^2 + b^2

foci at (sqrt(20), 0) and (sqrt(20), 0)

 sqrt(20)^2 = 16 + b^2

  20 - 16 = b^2

     b^2 = 4

       b = ± 2

   x^2/16 - y^2 /4 = 1