In this problem, we have an equation of the form
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]where
(h,k) is the center of the hyperbola
step 1
Find out the center
The center is the midpoint between the foci or between the vertices
the x-coordinate of the center is
x=(2+10)/2=6
the y-coordinate of the center is -5 (the same y-coordinate of the foci)
(h,k)=(6,-5)
step 2
Find out the value of a
Remember that
The coordinates of the vertices are
(h+a,k) and (h-a,k) ----------> (2,-5) and (10,-5)
so
h+a=2 -----> 6+a=2 --------> -4
