Find dy dx , when x=a and y=b - Vidyadip

Question

Find $\frac{\text{dy}}{\text{dx}},$ when
$\text{x}=\text{a}\cos\theta$ and $\text{y}=\text{b}\sin\theta$

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Answer

We have, $\text{x}=\text{a}\cos \theta$ and $\text{y}=\text{b}\cos\theta$
$\Rightarrow\frac{\text{dx}}{\text{d}\theta}=-\text{a}\sin\theta$ and $\frac{\text{dy}}{d\theta}=\text{b}\cos\theta$
$\therefore\frac{\text{dy}}{{\text{d}}\theta}=\frac{\frac{\text{dy}}{\text{d}\theta}}{\frac{\text{dx}}{\text{d}\theta}}=\frac{\text{b}\cos\theta}{-\text{a}\sin\theta}=\frac{-\text{b}}{\text{a}}\cot\theta$

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