A particle is moving along a hyberbola xy = 12. As it reaches the point (6,2), the y-coordinate is decreasing at a rate of 3cm/s. How fast is the x-coordinate of the point changing at that instant?

Answer 1

if xy = 12 then (dx/dt)y + x(dy/dt) = 0 or dx/dt = -(x/y)dy/dt

Substituting the given values dx/dt = -(6/2)(-3) = 9 m/s