A hedge is to be constructed in the shape of a hyperbola nea

A hedge is to be constructed in the shape of a hyperbola near a fountain at the center of a yard. The hedge will follow the asymptotes y = 3x and y = 3x, and its closest distance to the center fountain is 6 yards. Find the equation of the hyperbola. (Assume the x-axis is the transverse axis of the hyperbola centered at the origin.)

Solution

asymtotes :y = +/- (b/a)x

y = +/- 3x

b/a = 3 ----(1)

a = 6

b = 18

x^2/a^2 - y^2/b^2 = 1

x^2/36 - y^2/324 =1 ( equation of the hyperbola)