Question

If \[\frac{dy}{dx}\] when \[x = a \cos \theta \text{ and } y = b \sin \theta\] ?

Answer 1

\[\text{ We have, x } = a \cos\theta \ \text{ and } y = b \sin\theta\]

\[ \Rightarrow \frac{dx}{d\theta} = - a \sin\theta \text{ and } \frac{dy}{d\theta} = b \cos\theta\]

\[ \therefore \frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}} = \frac{b \cos\theta}{- a \sin\theta} = - \frac{b}{a}\cot\theta\]