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Question Number 31820 by mondodotto@gmail.com last updated on 15/Mar/18

Answered by mrW2 last updated on 15/Mar/18

$$\left(i\right)$$$$\frac{dx}{d\theta }=-4\sin \theta$$$$\frac{dy}{d\theta }=3\cos \theta$$$$\Rightarrow \frac{dy}{dx}=\frac{dy}{d\theta }\times \frac{1}{\frac{dx}{d\theta }}=-\frac{3\cos \theta }{4\sin \theta }$$$$\left(ii\right)$$$$(y-3\sin \theta )=\frac{4\sin \theta }{3\cos \theta }(x-4\cos \theta )$$$$\left(iii\right)$$$$(y-3\sin \frac{\pi }{4})=\frac{4}{3}(x-4\cos \frac{\pi }{4})$$$$(y-\frac{3\sqrt{2}}{2})=\frac{4}{3}(x-2\sqrt{2})$$$$\Rightarrow y=\frac{4x}{3}-\frac{7\sqrt{2}}{6}$$$$\left(iv\right)$$$$(2\sqrt{2},\frac{3\sqrt{2}}{2})$$

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