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Question

Let S be the set of points whose abscissas and ordinates are natural numbers. Let PS 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
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B
3
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C
5
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D
11
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Solution

The correct option is B 3
As we know, distance is minimum, if points are collinear
(x,y),(8,0),(0,12) are collinear


x(12)+8(12y)=0
12x+968y=0
3x+2y24=0
y=1232x
As x and y are natural number. Thus, possibles solutions are (2,9),(4,6),(6,3)
3 points are possible.

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