A curve $C$ has parametric equations $x=t-{{ an }^{-1}}\left( 2t-1 ight)$, $y=2t+1$, for $-2\le t

Question

A curve $C$ has parametric equations $x=t-{{	an }^{-1}}\left( 2t-1 ight)$, $y=2t+1$, for $-2\le t\le 3$. Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=2\left[ \frac{{{\left( 2t-1 ight)}^{2}}+1}{{{\left( 2t-1 ight)}^{2}}-1} ight]$. [2] Hence find the equations of the tangents to $C$ which are parallel to the $y$-axis. Leave your answers in exact form. [3] The line $y=4x$ cuts $C$ at the point $P$. The normal to $C$ at $P$ meets the $x$-axis at the point $Q$. Find the coordinates of $Q$. [5]

Accepted Answer

$Q = (-3.5, 0)$

2022 VJC J1 MYE Q6

2022 VJC J1 MYE Q6

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