Question

If \(x\) and \(y\) are connected parametrically by the equation,without eliminating the parameter,find \(\frac{dy}{dx}\).
\(x= a\,cos\,θ,y=b\,cos\,θ\)

Answer 1

The correct answer is \(∴\frac{dy}{dx}=\frac{(\frac{dy}{dθ})}{(\frac{dx}{dθ})}=\frac{-bsinθ}{-asinθ}=\frac{b}{a}\)
The given equations are \(x= a\,cos\,θ,y=b\,cos\,θ\)
Then,\(\frac{dx}{dθ}=\frac{d}{dθ}(a\,cos\,θ)=a(-sin\,θ))=-a\,sin\,θ\)
\(\frac{dy}{dθ}=\frac{d}{dθ}(b\,cos\,θ)=b(-sinθ)=-bsinθ\)
\(∴\frac{dy}{dx}=\frac{(\frac{dy}{dθ})}{(\frac{dx}{dθ})}=\frac{-bsinθ}{-asinθ}=\frac{b}{a}\)