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Question Number 25536 by tawa tawa last updated on 11/Dec/17

$$\mathrm{If}\mathrm{x}=2\sec \left(3\mathrm{t}\right)\mathrm{and}\mathrm{y}=4\tan \left(3\mathrm{t}\right),\mathrm{Show}\mathrm{that}\mathrm{y}=4({\mathrm{x}}^2-4)$$

Answered by prakash jain last updated on 11/Dec/17

$$x=2\sec 3t\Rightarrow \frac{x}{2}=\sec 3t$$$$y=4\tan 3t\Rightarrow \frac{y}{4}=\tan 3t$$$${\sec }^2\theta -{\tan }^2\theta =1$$$$\frac{x^2}{4}-\frac{y^2}{16}=1$$$$\frac{x^2-4}{4}=\frac{y^2}{16}$$$$\Rightarrow y^2=4(x^2-4)$$

Commented by tawa tawa last updated on 13/Dec/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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