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If $x=t^2$ and $y=2 t$ are parametric equations of a curve, then equation of the normal to the curve at $t=2$ is
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Verified Answer
The correct answer is:
$2 x+y-12=0$
Equation of normal at $t$
$\begin{aligned}
& (y-2 t)=\frac{-\mathrm{d} x}{\mathrm{~d} t}\left(x-t^2\right) \\
& \Rightarrow(y-2 t)=\frac{-2 t}{2}\left(x-t^2\right) \\
& \Rightarrow(y-4)=-2(x-4)[\text { for } t=2] \\
& \Rightarrow 2 x+y-12=0
\end{aligned}$
$\begin{aligned}
& (y-2 t)=\frac{-\mathrm{d} x}{\mathrm{~d} t}\left(x-t^2\right) \\
& \Rightarrow(y-2 t)=\frac{-2 t}{2}\left(x-t^2\right) \\
& \Rightarrow(y-4)=-2(x-4)[\text { for } t=2] \\
& \Rightarrow 2 x+y-12=0
\end{aligned}$
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