Question
If $x=a(1-\cos \theta), y=a(\theta+\sin \theta)$, prove that $\frac{d^{2} y}{d x^{2}}=-\frac{1}{a}$ at $\theta=\frac{\pi}{2}$
Step 1
We have $y=a(\theta+\sin \theta)$ and $x=a(1-\cos \theta)$. Show more…
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\begin{aligned} &\text { If } x=a(1-\cos \theta), y=a(\theta+\sin \theta) \text {, prove that }\\ &\frac{d^{2} y}{d x^{2}}=-\frac{1}{a} \text { at } \theta=\frac{\pi}{2} . \end{aligned}
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If $x=a(\theta+\sin \theta), y=a(1+\cos \theta)$ prove that $\frac{d^{2} y}{d x^{2}}=-\frac{a}{y^{2}}$
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