Let $S$ be the set of points whose abscissas and ordinates are natural numbers. Let $P \in S$ such that the sum of the distance of $P$ from $(8,0)$ and $(0,12)$ is minimum among all elements in $S$. Then the number of such points $P$ in $S$ is

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Let $S$ be the set of points whose abscissas and ordinates are natural numbers. Let $P \in S$ such that the sum of the distance of $P$ from $(8,0)$ and $(0,12)$ is minimum among all elements in $S$. Then the number of such points $P$ in $S$ is

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deepak01 · Answer 1 · 2021-12-20T08:32:29+0000

Ans: (B)
Sum of distances will be minimum if $P,(8,0)$ and $(0,12)$ will collinear
$$
\begin{aligned}
&\therefore \frac{x}{8}+\frac{y}{12}=1 \Rightarrow y=12-\frac{3}{2} x \\
&\therefore(x, y) \equiv(2,9),(4,6),(6,3)
\end{aligned}
$$

Let \(S\) be the set of points whose abscissas and ordinates are natural numbers. Let \(P \in S\) such that the sum of the distance of \(P\) from \((8,0)\) and \((0,12)\) is minimum among all elements in \(S\). Then the number of such points \(P\) in \(S\) is

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