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,\(\frac{dx}{dt}=\frac{d}{dt}(4t)=4\)
\(\frac{dy}{dt}=\frac{d}{dt}(\frac{4}{t})=4.\frac{d}{dt}(\frac{1}{t})=4.(\frac{-1}{t^2})=\frac{-4}{t^2}\)
\(∴\frac{dy}{dx}=\frac{(\frac{dy}{dt})}{(\frac{dx}{dt})}=\frac{\frac{-4}{t^2}}{4}=\frac{-1}{t^2}\)