Question

Center at (4, 2), a vertex at (7, 2) , and an asymptote 3y = 4x-10, what is the equation of this hyperbola

Answer 1

center at (4,2)

vertex at (7,2) means
(x-4)^2/a^2 - (y-2)^2/b^2 = 1
slope of asymptote is 4/3 = b/a, so
a = 3
b = 4
(x-4)^2/9 - (y-2)^2/16 = 1