Question

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
(A) 1
(B) 3
(C) 5
(D) 11

Answer 1

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

Answer 2

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