Prove that

Question:

$x=t+\frac{1}{t}, y=t-\frac{1}{t}$

Solution:

Given,

x = t + 1/t, y = t – 1/t

Differentiating both the parametric functions w.r.t θ

$\frac{d x}{d t}=1-\frac{1}{t^{2}}, \frac{d y}{d t}=1+\frac{1}{t^{2}}$

$\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{1+\frac{1}{t^{2}}}{1-\frac{1}{t^{2}}}=\frac{t^{2}+1}{t^{2}-1}$

Thus, $\frac{d y}{d x}=\frac{t^{2}+1}{t^{2}-1}$.

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