Take ST line as x-axis or major axis of hyperbola.
Midpoint ST is hyperbola's center C.
CS=CT=150 miles = c to focus S or T.
Length of major axis =2a=37.2 miles.
Length of minor axis/2= b = sqrt(c^2-a^2)=sqrt(150^2-(37.2/2)^2) = 148.842 miles.
Equation of hyperbola with center at C: ((x-x0)/a)^2 -((y-y0)/b)^2 = 1.
(x0,y0)=(0,0)= Point C