A curve $C$ has parametric equations $x=t+\frac{1}{t}$, $y=t-\frac{1}{t}$ Find a Cartesian equation

Question

A curve $C$ has parametric equations $x=t+\frac{1}{t}$, $y=t-\frac{1}{t}$ Find a Cartesian equation of $C$. Sketch $C$, giving the coordinates of any points where $C$ crosses the $x$- and $y$-axes and the equations of any asymptotes. The point $P$ on the curve has parameter $p$. Show that the straight line, $\ell $, with equation $\left( {{p}^{2}}+1 \right)x-\left( {{p}^{2}}-1 \right)y=4p$ cuts the curve only at $P$. [6]

Accepted Answer

(a) $\frac{{{x}^{2}}}{4}=\frac{{{y}^{2}}}{4}\Rightarrow y\pm x$

N2010 P1 Q11 [Modified]

N2010 P1 Q11 [Modified]

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