Question

A point is in a motion along a hyperbola `y = 10/x` so that its abscissa x increases uniformly at a rate of 1 unit per second. Then the rate of change of its ordinate, when the point passes through (5, 2) ______ 

विकल्प

• increases at the rate of `1/2` unit per second

• decreases at the rate of `1/2` unit per second

• decreases at the rate of `2/5` unit per second

• increases at the rate of `2/5` unit per second

Answer 1

A point is in a motion along a hyperbola `y = 10/x` so that its abscissa x increases uniformly at a rate of 1 unit per second. Then the rate of change of its ordinate, when the point passes through (5, 2) decreases at the rate of `2/5` unit per second.

Explanation:

`y = 10/x`

∴ `dy/dx = (-10)/x^2 . dx/dt` ..............(i)

Given that `dx/dt = 1`

⇒ `dy/dt = (-10)/x^2`

When the point passes through (5, 2), we have x = 5.

∴ `dy/dt = (-10)/5^2 = (-2)/5`

∴ The ordinate decreases at the rate of `2/5` unit per second.