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Question

Let A be the set of all points (α,β) such that the area of triangle formed by the points (5,6),(3,2) and (α,β) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is

A
85
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B
165
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C
45
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D
125
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Solution

The correct option is A 85
12∣ ∣αβ1561321∣ ∣=12
|4α2β8|=24
|2αβ4|=12
Locus =2xy4=12,2xy4=12
2xy16=0 or 2xy+8=0
Required length = minimum perpendicular distance from origin
=min{165,85}=85

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