SOLUTION: Find the equation of hyperbola given the conditions: Vertices: (13,0), (-1,0); asymptotes: y = x - 6 and y = -x + 6

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of hyperbola given the conditions: Vertices: (13,0), (-1,0); asymptotes: y = x - 6 and y = -x + 6      Log On


   

Question 1198403: Find the equation of hyperbola given the conditions:
Vertices: (13,0), (-1,0); asymptotes: y = x - 6 and y = -x + 6
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of a hyperbola is

%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2+%2Fb%5E2=1, where (h,k) is the center, a and b are the lengths of the semi-major and the semi-minor axes.
given:
Vertices: (13,0), (-1,0)
asymptotes: y+=+x+-+6 and y+=+-x+%2B+6
Vertices are at (h%2B-a,k)
so, k=0
h%2Ba=13....eq.1
h-a=-1.....eq.2
--------------------add
2h=12
h=6
the center is at (6,0)
the
6%2Ba=13
a=13-6
a=7
take into account different properties of a hyperbola:
b%2Fa=1
b%2F7=1
b=7
the equation of hyperbola is:
%28x-6%29%5E2%2F7%5E2+-+%28y-0%29%5E2+%2F7%5E2=1
%28x-6%29%5E2%2F49+-+y%5E2+%2F49=1