SOLUTION: Write the equation of the hyperbola given the following information Vertices : (2, - 6); (- 4, - 6) Foci: (- 1 + sqrt(10), - 6), (- 1 - sqrt(10), - 6)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write the equation of the hyperbola given the following information Vertices : (2, - 6); (- 4, - 6) Foci: (- 1 + sqrt(10), - 6), (- 1 - sqrt(10), - 6)       Log On


   

Question 1187159: Write the equation of the hyperbola given the following information Vertices : (2, - 6); (- 4, - 6) Foci: (- 1 + sqrt(10), - 6), (- 1 - sqrt(10), - 6)
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the hyperbola given the following information
Vertices : (2, -6); (-4, -6)
Foci: (-1+%2B+sqrt%2810%29, -+6), (-1-sqrt%2810%29, -+6)
the canter is half way between
(h,k)=(%282-4%29%2F2,(-6-6%29%2F2)=(-1,-6)

a=distance+from+the+center+to+vertex
=>a=3
Foci: (-1+%2B+sqrt%2810%29, -+6), (-1-sqrt%2810%29, -+6)
c=distance from the center to foci
c=sqrt%28%28-+1+%2B+sqrt%2810%29%2B1%29%5E2%28-6%2B6%29%5E2%29=sqrt%28+10%29
c=sqrt%2810%29
b=sqrt%28c%5E2-a%5E2%29
b=sqrt%28%28sqrt%28+10%29%29%5E2-3%5E2%29
b=sqrt%2810-9%29
b=sqrt%281%29
b=1

your equation is:
%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1
%28x-2%29%5E2%2F3%5E2-%28y-%28-6%29%29%5E2%2F1%5E2=1
%28x-2%29%5E2%2F9-%28y%2B6%29%5E2=1




Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.

The correct form equation is


    %28x%2B1%29%5E2%2F9 - %28y%2B6%29%5E2 = 1.