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Question

Let $\mathrm{P}$ and $\mathrm{Q}$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$, respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval :

$\left(0, \frac{1}{4}\right)$
$\left(\frac{1}{2}, \frac{3}{4}\right)$
$\left(\frac{1}{4}, \frac{1}{2}\right)$
$\left(\frac{3}{4}, 1\right)$

Solution

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