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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
If x and y are connected parametrically by the equations given in Exercise without eliminating the parameter, Find $\frac{\text{dy}}{\text{dx}}.$
$\text{x}=\text{a}\cos\theta,\text{y}=\text{b}\cos\theta$
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Answer

The given equations are  $\text{x}=\text{a}\cos\theta\text{ and y}=\text{b}\cos\theta$
Then, $\frac{\text{dx}}{\text{d}\theta}=\frac{\text{d}}{\text{d}\theta}(\text{a}\cos\theta)=\text{a}(-\sin\theta)=-\text{a}\sin\theta$
$\frac{\text{dy}}{\text{d}\theta}=\frac{\text{d}}{\text{d}\theta}(\text{b}\cos\theta)=\text{b}(-\sin\theta)=-\text{b}\sin\theta$
$\therefore\ \frac{\text{dy}}{\text{dx}}=\frac{\Big(\frac{\text{dy}}{\text{d}\theta}\Big)}{\Big(\frac{\text{dx}}{\text{d}\theta}\Big)}=\frac{-\text{b}\sin\theta}{-\text{a}\sin\theta}=\frac{\text{b}}{\text{a}}$

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