# If $x$ and $y$ are connected parametrically by the equations given in $x = a \cos \theta, y = b \cos \theta$ without eliminating the parameter, Find $\frac{\large dy}{\large dx}$

$\begin{array}{1 1} \large\frac{3b}{2a} \\\large\frac{b}{2a} \\ \large\frac{-b}{a} \\ \large\frac{b}{a} \end{array}$

Toolbox:
• By chain rule we have $\large\frac{dy}{dx}=\frac{dy}{d\theta}$$\times$$\large\frac{d\theta}{dx}$
Step 1:
Given :
$x=a\cos\theta$
Differentiate with respect to $\theta$
$\large\frac{dx}{d\theta}$$=a(-\sin\theta) f'(t)=-a\sin\theta Step 2: y=b\cos\theta Differentiate with respect to \theta \large\frac{dy}{d\theta}$$=b(-\sin\theta)$
$g'(t)=-b\sin\theta$
Step 3:
$\large\frac{dy}{dx}=\frac{dy}{d\theta}$$\times$$\large\frac{d\theta}{dx}$