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,$\frac{dx}{dθ}=\frac{d}{dθ}(a\,cos\,θ)=a(-sin\,θ))=-a\,sin\,θ$
$\frac{dy}{dθ}=\frac{d}{dθ}(b\,cos\,θ)=b(-sinθ)=-bsinθ$
$∴\frac{dy}{dx}=\frac{(\frac{dy}{dθ})}{(\frac{dx}{dθ})}=\frac{-bsinθ}{-asinθ}=\frac{b}{a}$