Question

If $x$ and $y$ are connected parametrically by the equation,without eliminating the parameter,find $\frac{dy}{dx}$.
$x=4t,y=\frac{4}{t}$

Answer 1

The correct answer is $\frac{-1}{t^2}$
The given equations are $x=4t,y=\frac{4}{t}$
Then,$\frac{dx}{dt}=\frac{d}{dt}(4t)=4$
$\frac{dy}{dt}=\frac{d}{dt}(\frac{4}{t})=4.\frac{d}{dt}(\frac{1}{t})=4.(\frac{-1}{t^2})=\frac{-4}{t^2}$
$∴\frac{dy}{dx}=\frac{(\frac{dy}{dt})}{(\frac{dx}{dt})}=\frac{\frac{-4}{t^2}}{4}=\frac{-1}{t^2}$