SOLUTION: Write an equation for the hyperbola with vertices (-10, 1) and (6,1) and foci (-12, 1) and (8,1).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation for the hyperbola with vertices (-10, 1) and (6,1) and foci (-12, 1) and (8,1).      Log On


   

Question 331973: Write an equation for the hyperbola with vertices (-10, 1) and (6,1) and foci (-12, 1) and (8,1).
Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
The vertices are at (-10,1) and (6,1). Note, there is a distance of 16 units between them. This means the center of the hyperbola is 8 units from either one.
Namely, at (-2,1).
There is a distance of 10 units from the center to a focus. This is c.
There is a distance of 8 units from the center to a vertex. This is a.
b is the vertical distance up the conjugate axis forming the auxiliary rectangle.
Since b=sqrt%28c%5E2-a%5E2%29, we have b=sqrt%2810%5E2-8%5E2%29=6
So, a%5E2=64 and b%5E2=36
The equation is:
%28x%2B2%29%5E2%2F64-%28y-1%29%5E2%2F36=1