Question

If x and y are connected parametrically by the equation, without eliminating the parameter, find dy/dx x=4t, y=4/t

Answer 1

Given, x = 4t and y = 4/t

$\bf{\underline{x=4t}}$
now, differentiate x with respect to t
dx/dt = 4 ------(1)

$\bf{\underline{y=\frac{4}{t}}}$
now , differentiate y with respect to t
dy/dt = -4/t² ------(2)

dividing equations (2) by (1),
{dy/dt}/{dx/dt} = {-4/t²}/{4} = -1/t²
dy/dx = -1/t²

hence, the value of $\bf{\frac{dy}{dx}=-\frac{1}{t^2}}$