SOLUTION: need help with this question. Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (1,-8), (1,-2) foci: (1,-10),(1,0)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: need help with this question. Find the standard form of the equation of the hyperbola with the given characteristics. vertices: (1,-8), (1,-2) foci: (1,-10),(1,0)       Log On


   

Question 444456: need help with this question.
Find the standard form of the equation of the hyperbola with the given characteristics.
vertices: (1,-8), (1,-2) foci: (1,-10),(1,0)
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi, Previously Posted

Standard Form of an Equation of an Hyperbola opening up and down is:

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

where Pt(h,k) is a center  with vertices 'b' units up and down from center.

vertices: (1,-8), (1,-2)  b = 6/2= 3 then Center is (1,-5) 

  %28y%2B5%29%5E2%2F9+-+%28x-1%29%5E2%2Fa%5E2+=+1

 foci: (1,-10),(1,0) sqrt%28+9+%2B+a%5E2%29+=+10%2F2+=+5 a^2 = 16

   %28y%2B5%29%5E2%2F9+-+%28x-1%29%5E2%2F16+=+1