Question

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x=4t,y=\frac{4}{t}.$

Answer 1

Given, $x=4t,y=\frac{4}{t}$

Differentiating w.r.t, we get $\frac{dx}{dt}=4and\frac{dy}{dt}=4(-1)t^{-2}$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{-4t^{-2}}{4}=-\frac{1}{t^2}(\because \frac{dy}{dx}=\frac{dy/dt}{dx/dt})$