How do you write a standard form equation for the hyperbola with foci are (-6,0) and (6,0) and the difference of the focal radii is 10?
As both the foci are on the x-axis, x-axis is the major axis of the hyperbola.
The difference between the focal radii = length of the major axis 2a = 10. So, a = 5.
The distance between the foci s(6, 0) and S'#(-6, 0) = 12 = major axis length 2 a x eccentricity = 2 a e = 10 e =12. So, e = 6/5.
The semi-transverse axis
The standard form of the equation is
here, it is